Daily Papers

Reward-based optimization algorithms require both exploration, to find rewards, and exploitation, to maximize performance. The need for efficient exploration is even more significant in sparse reward settings, in which performance feedback is given sparingly, thus rendering it unsuitable for guiding the search process. In this work, we introduce the SparsE Reward Exploration via Novelty and Emitters (SERENE) algorithm, capable of efficiently exploring a search space, as well as optimizing rewards found in potentially disparate areas. Contrary to existing emitters-based approaches, SERENE separates the search space exploration and reward exploitation into two alternating processes. The first process performs exploration through Novelty Search, a divergent search algorithm. The second one exploits discovered reward areas through emitters, i.e. local instances of population-based optimization algorithms. A meta-scheduler allocates a global computational budget by alternating between the two processes, ensuring the discovery and efficient exploitation of disjoint reward areas. SERENE returns both a collection of diverse solutions covering the search space and a collection of high-performing solutions for each distinct reward area. We evaluate SERENE on various sparse reward environments and show it compares favorably to existing baselines.

Fine-grained visual reasoning remains a core challenge for multimodal large language models (MLLMs). The recently introduced ReasonMap highlights this gap by showing that even advanced MLLMs struggle with spatial reasoning in structured and information-rich settings such as transit maps, a task of clear practical and scientific importance. However, standard reinforcement learning (RL) on such tasks is impeded by sparse rewards and unstable optimization. To address this, we first construct ReasonMap-Plus, an extended dataset that introduces dense reward signals through Visual Question Answering (VQA) tasks, enabling effective cold-start training of fine-grained visual understanding skills. Next, we propose RewardMap, a multi-stage RL framework designed to improve both visual understanding and reasoning capabilities of MLLMs. RewardMap incorporates two key designs. First, we introduce a difficulty-aware reward design that incorporates detail rewards, directly tackling the sparse rewards while providing richer supervision. Second, we propose a multi-stage RL scheme that bootstraps training from simple perception to complex reasoning tasks, offering a more effective cold-start strategy than conventional Supervised Fine-Tuning (SFT). Experiments on ReasonMap and ReasonMap-Plus demonstrate that each component of RewardMap contributes to consistent performance gains, while their combination yields the best results. Moreover, models trained with RewardMap achieve an average improvement of 3.47% across 6 benchmarks spanning spatial reasoning, fine-grained visual reasoning, and general tasks beyond transit maps, underscoring enhanced visual understanding and reasoning capabilities.

In the Reinforcement Learning (RL) framework, the learning is guided through a reward signal. This means that in situations of sparse rewards the agent has to focus on exploration, in order to discover which action, or set of actions leads to the reward. RL agents usually struggle with this. Exploration is the focus of Quality-Diversity (QD) methods. In this thesis, we approach the problem of sparse rewards with these algorithms, and in particular with Novelty Search (NS). This is a method that only focuses on the diversity of the possible policies behaviors. The first part of the thesis focuses on learning a representation of the space in which the diversity of the policies is evaluated. In this regard, we propose the TAXONS algorithm, a method that learns a low-dimensional representation of the search space through an AutoEncoder. While effective, TAXONS still requires information on when to capture the observation used to learn said space. For this, we study multiple ways, and in particular the signature transform, to encode information about the whole trajectory of observations. The thesis continues with the introduction of the SERENE algorithm, a method that can efficiently focus on the interesting parts of the search space. This method separates the exploration of the search space from the exploitation of the reward through a two-alternating-steps approach. The exploration is performed through NS. Any discovered reward is then locally exploited through emitters. The third and final contribution combines TAXONS and SERENE into a single approach: STAX. Throughout this thesis, we introduce methods that lower the amount of prior information needed in sparse rewards settings. These contributions are a promising step towards the development of methods that can autonomously explore and find high-performance policies in a variety of sparse rewards settings.

Autonomous robots exploring unknown areas face a significant challenge -- navigating effectively without prior maps and with limited external feedback. This challenge intensifies in sparse reward environments, where traditional exploration techniques often fail. In this paper, we introduce TopoNav, a novel framework that empowers robots to overcome these constraints and achieve efficient, adaptable, and goal-oriented exploration. TopoNav's fundamental building blocks are active topological mapping, intrinsic reward mechanisms, and hierarchical objective prioritization. Throughout its exploration, TopoNav constructs a dynamic topological map that captures key locations and pathways. It utilizes intrinsic rewards to guide the robot towards designated sub-goals within this map, fostering structured exploration even in sparse reward settings. To ensure efficient navigation, TopoNav employs the Hierarchical Objective-Driven Active Topologies framework, enabling the robot to prioritize immediate tasks like obstacle avoidance while maintaining focus on the overall goal. We demonstrate TopoNav's effectiveness in simulated environments that replicate real-world conditions. Our results reveal significant improvements in exploration efficiency, navigational accuracy, and adaptability to unforeseen obstacles, showcasing its potential to revolutionize autonomous exploration in a wide range of applications, including search and rescue, environmental monitoring, and planetary exploration.

Learning optimal policies in sparse rewards settings is difficult as the learning agent has little to no feedback on the quality of its actions. In these situations, a good strategy is to focus on exploration, hopefully leading to the discovery of a reward signal to improve on. A learning algorithm capable of dealing with this kind of settings has to be able to (1) explore possible agent behaviors and (2) exploit any possible discovered reward. Efficient exploration algorithms have been proposed that require to define a behavior space, that associates to an agent its resulting behavior in a space that is known to be worth exploring. The need to define this space is a limitation of these algorithms. In this work, we introduce STAX, an algorithm designed to learn a behavior space on-the-fly and to explore it while efficiently optimizing any reward discovered. It does so by separating the exploration and learning of the behavior space from the exploitation of the reward through an alternating two-steps process. In the first step, STAX builds a repertoire of diverse policies while learning a low-dimensional representation of the high-dimensional observations generated during the policies evaluation. In the exploitation step, emitters are used to optimize the performance of the discovered rewarding solutions. Experiments conducted on three different sparse reward environments show that STAX performs comparably to existing baselines while requiring much less prior information about the task as it autonomously builds the behavior space.

Robots in many real-world settings have access to force/torque sensors in their gripper and tactile sensing is often necessary in tasks that involve contact-rich motion. In this work, we leverage surprise from mismatches in touch feedback to guide exploration in hard sparse-reward reinforcement learning tasks. Our approach, Touch-based Curiosity (ToC), learns what visible objects interactions are supposed to "feel" like. We encourage exploration by rewarding interactions where the expectation and the experience don't match. In our proposed method, an initial task-independent exploration phase is followed by an on-task learning phase, in which the original interactions are relabeled with on-task rewards. We test our approach on a range of touch-intensive robot arm tasks (e.g. pushing objects, opening doors), which we also release as part of this work. Across multiple experiments in a simulated setting, we demonstrate that our method is able to learn these difficult tasks through sparse reward and curiosity alone. We compare our cross-modal approach to single-modality (touch- or vision-only) approaches as well as other curiosity-based methods and find that our method performs better and is more sample-efficient.

What fundamental properties of reward functions enable efficient sparse-reward reinforcement learning? We address this question through the lens of low-rank structure in reward matrices, showing that such structure induces a sharp transition from exponential to polynomial sample complexity, the first result of this kind for sparse-reward RL. We introduce Policy-Aware Matrix Completion (PAMC), which connects matrix completion theory with reinforcement learning via a new analysis of policy-dependent sampling. Our framework provides: (i) impossibility results for general sparse reward observation, (ii) reward-free representation learning from dynamics, (iii) distribution-free confidence sets via conformal prediction, and (iv) robust completion guarantees that degrade gracefully when low-rank structure is only approximate. Empirically, we conduct a pre-registered evaluation across 100 systematically sampled domains, finding exploitable structure in over half. PAMC improves sample efficiency by factors between 1.6 and 2.1 compared to strong exploration, structured, and representation-learning baselines, while adding only about 20 percent computational overhead.These results establish structural reward learning as a promising new paradigm, with immediate implications for robotics, healthcare, and other safety-critical, sample-expensive applications.

Diffusion models have achieved remarkable success in text-to-image generation. However, their practical applications are hindered by the misalignment between generated images and corresponding text prompts. To tackle this issue, reinforcement learning (RL) has been considered for diffusion model fine-tuning. Yet, RL's effectiveness is limited by the challenge of sparse reward, where feedback is only available at the end of the generation process. This makes it difficult to identify which actions during the denoising process contribute positively to the final generated image, potentially leading to ineffective or unnecessary denoising policies. To this end, this paper presents a novel RL-based framework that addresses the sparse reward problem when training diffusion models. Our framework, named B^2-DiffuRL, employs two strategies: Backward progressive training and Branch-based sampling. For one thing, backward progressive training focuses initially on the final timesteps of denoising process and gradually extends the training interval to earlier timesteps, easing the learning difficulty from sparse rewards. For another, we perform branch-based sampling for each training interval. By comparing the samples within the same branch, we can identify how much the policies of the current training interval contribute to the final image, which helps to learn effective policies instead of unnecessary ones. B^2-DiffuRL is compatible with existing optimization algorithms. Extensive experiments demonstrate the effectiveness of B^2-DiffuRL in improving prompt-image alignment and maintaining diversity in generated images. The code for this work is available.

Large Language Reasoning Models have demonstrated remarkable success on static tasks, yet their application to multi-round agentic planning in interactive environments faces two fundamental challenges. First, the intractable credit assignment problem renders conventional reinforcement learning ineffective in sparse-reward settings. Second, the computational overhead of verbose, step-by-step reasoning histories is prohibitive. To address these challenges, we propose BPO, a three-stage framework (bootstrapping, extrapolation, and refinement) that establishes a self-improving data flywheel to develop robust reasoning models for long-horizon, sparse-reward environments. Our framework first bootstraps efficient reasoning using the proposed planning quaternions with long-short chain-of-thought fusion. It then extrapolates to out-of-distribution tasks through complexity-stratified curriculum learning. Finally, the model iteratively refines itself by learning exclusively on experiences selected via reward-gated rejection sampling. Experiments on ALFWorld, ScienceWorld, and WebShop demonstrate that our approach achieves state-of-the-art with significant token efficiency, providing a new recipe for reasoning models in agentic planning.

We investigated Agentic RL with large language models on the TravelPlanner benchmark. Our approach, Planner-R1, achieved a 56.9\% final-pass rate with only 180 training queries, a 2.7times improvement over GPT-5's 21.2% baseline and the strongest agentic result on the public leaderboard. A central finding was that smaller models (8B) were highly responsive to reward shaping: with dense process-level signals, they reached competitive performance while being 3.5times more compute-efficient and 1.5times more memory-efficient than 32B models. Larger models were more robust under sparse rewards but exhibited smaller relative gains from shaping and higher variance across runs. While curriculum learning offered no significant benefit, shaped rewards consistently amplified learning dynamics, making 8B models the most efficient setting for agentic RL. Crucially, these gains did not come at the cost of overfitting: fine-tuned models mostly maintained or exceeded baseline performance on out-of-domain tasks, including Multi-IF, NaturalPlan, and tau-Bench. These results establish reward shaping as a decisive lever for scaling agentic RL, highlight the competitive strength of smaller models, and demonstrate that efficiency can be achieved without sacrificing generalization.

Intrinsic reward shaping has emerged as a prevalent approach to solving hard-exploration and sparse-rewards environments in reinforcement learning (RL). While single intrinsic rewards, such as curiosity-driven or novelty-based methods, have shown effectiveness, they often limit the diversity and efficiency of exploration. Moreover, the potential and principle of combining multiple intrinsic rewards remains insufficiently explored. To address this gap, we introduce HIRE (Hybrid Intrinsic REward), a flexible and elegant framework for creating hybrid intrinsic rewards through deliberate fusion strategies. With HIRE, we conduct a systematic analysis of the application of hybrid intrinsic rewards in both general and unsupervised RL across multiple benchmarks. Extensive experiments demonstrate that HIRE can significantly enhance exploration efficiency and diversity, as well as skill acquisition in complex and dynamic settings.

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts. This paper proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through Outcome REwArd-based reinforcement Learning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible. We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments. This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples. To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning. With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500. Our investigation also indicates the importance of initial policy models and training queries for RL. Code, models, and data will be released to benefit future researchhttps://github.com/InternLM/OREAL.

Designing reward functions is a longstanding challenge in reinforcement learning (RL); it requires specialized knowledge or domain data, leading to high costs for development. To address this, we introduce Text2Reward, a data-free framework that automates the generation of dense reward functions based on large language models (LLMs). Given a goal described in natural language, Text2Reward generates dense reward functions as an executable program grounded in a compact representation of the environment. Unlike inverse RL and recent work that uses LLMs to write sparse reward codes, Text2Reward produces interpretable, free-form dense reward codes that cover a wide range of tasks, utilize existing packages, and allow iterative refinement with human feedback. We evaluate Text2Reward on two robotic manipulation benchmarks (ManiSkill2, MetaWorld) and two locomotion environments of MuJoCo. On 13 of the 17 manipulation tasks, policies trained with generated reward codes achieve similar or better task success rates and convergence speed than expert-written reward codes. For locomotion tasks, our method learns six novel locomotion behaviors with a success rate exceeding 94%. Furthermore, we show that the policies trained in the simulator with our method can be deployed in the real world. Finally, Text2Reward further improves the policies by refining their reward functions with human feedback. Video results are available at https://text-to-reward.github.io

Automatically synthesizing dense rewards from natural language descriptions is a promising paradigm in reinforcement learning (RL), with applications to sparse reward problems, open-ended exploration, and hierarchical skill design. Recent works have made promising steps by exploiting the prior knowledge of large language models (LLMs). However, these approaches suffer from important limitations: they are either not scalable to problems requiring billions of environment samples, due to requiring LLM annotations for each observation, or they require a diverse offline dataset, which may not exist or be impossible to collect. In this work, we address these limitations through a combination of algorithmic and systems-level contributions. We propose \oni, a distributed architecture that simultaneously learns an RL policy and an intrinsic reward function using LLM feedback. Our approach annotates the agent's collected experience via an asynchronous LLM server, which is then distilled into an intrinsic reward model. We explore a range of algorithmic choices for reward modeling with varying complexity, including hashing, classification, and ranking models. By studying their relative tradeoffs, we shed light on questions regarding intrinsic reward design for sparse reward problems. Our approach achieves state-of-the-art performance across a range of challenging, sparse reward tasks from the NetHack Learning Environment in a simple unified process, solely using the agent's gathered experience, without requiring external datasets. We make our code available at https://github.com/facebookresearch/oni.

Many reinforcement learning environments (e.g., Minecraft) provide only sparse rewards that indicate task completion or failure with binary values. The challenge in exploration efficiency in such environments makes it difficult for reinforcement-learning-based agents to learn complex tasks. To address this, this paper introduces an advanced learning system, named Auto MC-Reward, that leverages Large Language Models (LLMs) to automatically design dense reward functions, thereby enhancing the learning efficiency. Auto MC-Reward consists of three important components: Reward Designer, Reward Critic, and Trajectory Analyzer. Given the environment information and task descriptions, the Reward Designer first design the reward function by coding an executable Python function with predefined observation inputs. Then, our Reward Critic will be responsible for verifying the code, checking whether the code is self-consistent and free of syntax and semantic errors. Further, the Trajectory Analyzer summarizes possible failure causes and provides refinement suggestions according to collected trajectories. In the next round, Reward Designer will further refine and iterate the dense reward function based on feedback. Experiments demonstrate a significant improvement in the success rate and learning efficiency of our agents in complex tasks in Minecraft, such as obtaining diamond with the efficient ability to avoid lava, and efficiently explore trees and animals that are sparse in the plains biome.

Reinforcement learning (RL) in long horizon and sparse reward tasks is notoriously difficult and requires a lot of training steps. A standard solution to speed up the process is to leverage additional reward signals, shaping it to better guide the learning process. In the context of language-conditioned RL, the abstraction and generalisation properties of the language input provide opportunities for more efficient ways of shaping the reward. In this paper, we leverage this idea and propose an automated reward shaping method where the agent extracts auxiliary objectives from the general language goal. These auxiliary objectives use a question generation (QG) and question answering (QA) system: they consist of questions leading the agent to try to reconstruct partial information about the global goal using its own trajectory. When it succeeds, it receives an intrinsic reward proportional to its confidence in its answer. This incentivizes the agent to generate trajectories which unambiguously explain various aspects of the general language goal. Our experimental study shows that this approach, which does not require engineer intervention to design the auxiliary objectives, improves sample efficiency by effectively directing exploration.

Reinforcement learning from human feedback (RLHF) has been widely adopted to align language models (LMs) with human preference. Prior RLHF works typically take a bandit formulation, which, though intuitive, ignores the sequential nature of LM generation and can suffer from the sparse reward issue. While recent works propose dense token-level RLHF, treating each token as an action may be oversubtle to proper reward assignment. In this paper, we seek to get the best of both by training and utilizing a segment-level reward model, which assigns a reward to each semantically complete text segment that spans over a short sequence of tokens. For reward learning, our method allows dynamic text segmentation and compatibility with standard sequence-preference datasets. For effective RL-based LM training against segment reward, we generalize the classical scalar bandit reward normalizers into location-aware normalizer functions and interpolate the segment reward for further densification. With these designs, our method performs competitively on three popular RLHF benchmarks for LM policy: AlpacaEval 2.0, Arena-Hard, and MT-Bench. Ablation studies are conducted to further demonstrate our method.

Autonomous agents for long-sequence Graphical User Interface tasks are hindered by sparse rewards and the intractable credit assignment problem. To address these challenges, we introduce GUI-Shepherd, a Process Reward Model that provides dense, step-by-step feedback to guide agents. GUI-Shepherd is trained on a diverse large-scale data set of 52k interactions that features human-annotated scores and GPT-4o generated rationales, enabling it to serve both as a reward provider for RL training and as a verifier for inference. As far as we know, we are the first to conduct a systematic study of process supervision in GUI agents, across diverse settings from online long-horizon tasks to offline single-step prediction. On the online AndroidWorld benchmark, GUI-Shepherd improves success rate by 7.7 points via multi-turn online PPO, significantly outperforming Outcome Reward Model based competitors. When used as an inference verifier, it brings 5.1 points improvements. The benefits generalize to the offline AndroidControl benchmark, with gains of 2.2 points as a reward provider and 4.3 points as a verifier. Collectively, our results establish that high-fidelity process supervision is critical for building more capable GUI agents and present a generalizable solution.

Reinforcement Learning from Human Feedback (RLHF) has been credited as the key advance that has allowed Large Language Models (LLMs) to effectively follow instructions and produce useful assistance. Classically, this involves generating completions from the LLM in response to a query before using a separate reward model to assign a score to the full completion. As an auto-regressive process, the LLM has to take many "actions" (selecting individual tokens) and only receives a single, sparse reward at the end of an episode, a setup that is known to be difficult to optimise in traditional reinforcement learning. In this work we leverage the fact that the reward model contains more information than just its scalar output, in particular, it calculates an attention map over tokens as part of the transformer architecture. We use these attention weights to redistribute the reward along the whole completion, effectively densifying the signal and highlighting the most important tokens, all without incurring extra computational cost or requiring any additional modelling. We demonstrate that, theoretically, this approach is equivalent to potential-based reward shaping, ensuring that the optimal policy remains unchanged. Empirically, we show that it stabilises training, accelerates the rate of learning, and, in practical cases, may lead to better local optima.

Reward machines (RMs) are a recent formalism for representing the reward function of a reinforcement learning task through a finite-state machine whose edges encode subgoals of the task using high-level events. The structure of RMs enables the decomposition of a task into simpler and independently solvable subtasks that help tackle long-horizon and/or sparse reward tasks. We propose a formalism for further abstracting the subtask structure by endowing an RM with the ability to call other RMs, thus composing a hierarchy of RMs (HRM). We exploit HRMs by treating each call to an RM as an independently solvable subtask using the options framework, and describe a curriculum-based method to learn HRMs from traces observed by the agent. Our experiments reveal that exploiting a handcrafted HRM leads to faster convergence than with a flat HRM, and that learning an HRM is feasible in cases where its equivalent flat representation is not.

Reinforcement learning (RL) can align language models with non-differentiable reward signals, such as human preferences. However, a major challenge arises from the sparsity of these reward signals - typically, there is only one reward for the entire generation. This sparsity of rewards can lead to inefficient and unstable learning. In this paper, we introduce a novel framework leveraging the critique ability of LLMs to produce dense rewards throughout the learning process. Our approach incorporates a critic language model alongside the policy model. This critic is prompted with the task description, question, policy model's output, and environment's reward signal as input, and provides token or span-level dense rewards that reflect the quality of each segment of the output. We assess our approach on three text generation tasks: sentiment control, language model detoxification, and summarization. Experimental results show that incorporating artificial dense rewards in training yields consistent performance gains over the PPO baseline with holistic rewards. Furthermore, in a setting where the same model serves as both policy and critic, we demonstrate that "self-critique" rewards also boost learning efficiency.

The success of many RL techniques heavily relies on human-engineered dense rewards, which typically demand substantial domain expertise and extensive trial and error. In our work, we propose DrS (Dense reward learning from Stages), a novel approach for learning reusable dense rewards for multi-stage tasks in a data-driven manner. By leveraging the stage structures of the task, DrS learns a high-quality dense reward from sparse rewards and demonstrations if given. The learned rewards can be reused in unseen tasks, thus reducing the human effort for reward engineering. Extensive experiments on three physical robot manipulation task families with 1000+ task variants demonstrate that our learned rewards can be reused in unseen tasks, resulting in improved performance and sample efficiency of RL algorithms. The learned rewards even achieve comparable performance to human-engineered rewards on some tasks. See our project page (https://sites.google.com/view/iclr24drs) for more details.

Model-based reinforcement learning (MBRL) has gained much attention for its ability to learn complex behaviors in a sample-efficient way: planning actions by generating imaginary trajectories with predicted rewards. Despite its success, we found that surprisingly, reward prediction is often a bottleneck of MBRL, especially for sparse rewards that are challenging (or even ambiguous) to predict. Motivated by the intuition that humans can learn from rough reward estimates, we propose a simple yet effective reward smoothing approach, DreamSmooth, which learns to predict a temporally-smoothed reward, instead of the exact reward at the given timestep. We empirically show that DreamSmooth achieves state-of-the-art performance on long-horizon sparse-reward tasks both in sample efficiency and final performance without losing performance on common benchmarks, such as Deepmind Control Suite and Atari benchmarks.

Offline reinforcement learning (RL) offers a promising direction for learning policies from pre-collected datasets without requiring further interactions with the environment. However, existing methods struggle to handle out-of-distribution (OOD) extrapolation errors, especially in sparse reward or scarce data settings. In this paper, we propose a novel training algorithm called Conservative Density Estimation (CDE), which addresses this challenge by explicitly imposing constraints on the state-action occupancy stationary distribution. CDE overcomes the limitations of existing approaches, such as the stationary distribution correction method, by addressing the support mismatch issue in marginal importance sampling. Our method achieves state-of-the-art performance on the D4RL benchmark. Notably, CDE consistently outperforms baselines in challenging tasks with sparse rewards or insufficient data, demonstrating the advantages of our approach in addressing the extrapolation error problem in offline RL.

Natural language is often the easiest and most convenient modality for humans to specify tasks for robots. However, learning to ground language to behavior typically requires impractical amounts of diverse, language-annotated demonstrations collected on each target robot. In this work, we aim to separate the problem of what to accomplish from how to accomplish it, as the former can benefit from substantial amounts of external observation-only data, and only the latter depends on a specific robot embodiment. To this end, we propose Video-Language Critic, a reward model that can be trained on readily available cross-embodiment data using contrastive learning and a temporal ranking objective, and use it to score behavior traces from a separate actor. When trained on Open X-Embodiment data, our reward model enables 2x more sample-efficient policy training on Meta-World tasks than a sparse reward only, despite a significant domain gap. Using in-domain data but in a challenging task generalization setting on Meta-World, we further demonstrate more sample-efficient training than is possible with prior language-conditioned reward models that are either trained with binary classification, use static images, or do not leverage the temporal information present in video data.

Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call Multi-level Actor-Critic (MAC), is developed especially for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it, therefore, is readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to the state-of-the-art AC algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.

Reinforcement learning from human feedback (RLHF) has been crucial in aligning large language models (LLMs) with human values. Traditionally, RLHF involves generating responses to a query and using a reward model to assign a reward to the entire response. However, this approach faces challenges due to its reliance on a single, sparse reward, which makes it challenging for the model to identify which parts of the sequence contribute most significantly to the final reward. Recent methods have attempted to address this limitation by introducing token-level rewards. However, these methods often rely on either a trained credit assignment model or AI annotators, raising concerns about the quality and reliability of the rewards. In this paper, we propose token-level reward regularization (T-REG), a novel approach that leverages both sequence-level and token-level rewards for preference optimization. Harnessing the self-refinement capabilities of LLMs, our method uses contrastive prompting to enable LLMs to self-generate token-level rewards. These self-generated rewards then act as reward regularization, guiding the model to more effectively distribute sequence-level rewards across tokens. This facilitates better token-level credit assignment and enhances alignment performance. Experiments on the instruction following benchmarks, including Alpaca Eval 2 and Arena-Hard, show that our method consistently outperforms baseline methods by up to 3.8% and 4.4%, respectively. We will release the code and models at https://github.com/wzhouad/T-REG.

Intelligent creatures can explore their environments and learn useful skills without supervision. In this paper, we propose DIAYN ('Diversity is All You Need'), a method for learning useful skills without a reward function. Our proposed method learns skills by maximizing an information theoretic objective using a maximum entropy policy. On a variety of simulated robotic tasks, we show that this simple objective results in the unsupervised emergence of diverse skills, such as walking and jumping. In a number of reinforcement learning benchmark environments, our method is able to learn a skill that solves the benchmark task despite never receiving the true task reward. We show how pretrained skills can provide a good parameter initialization for downstream tasks, and can be composed hierarchically to solve complex, sparse reward tasks. Our results suggest that unsupervised discovery of skills can serve as an effective pretraining mechanism for overcoming challenges of exploration and data efficiency in reinforcement learning.

Sparse reward environments in reinforcement learning (RL) pose significant challenges for exploration, often leading to inefficient or incomplete learning processes. To tackle this issue, this work proposes a teacher-student RL framework that leverages Large Language Models (LLMs) as "teachers" to guide the agent's learning process by decomposing complex tasks into subgoals. Due to their inherent capability to understand RL environments based on a textual description of structure and purpose, LLMs can provide subgoals to accomplish the task defined for the environment in a similar fashion to how a human would do. In doing so, three types of subgoals are proposed: positional targets relative to the agent, object representations, and language-based instructions generated directly by the LLM. More importantly, we show that it is possible to query the LLM only during the training phase, enabling agents to operate within the environment without any LLM intervention. We assess the performance of this proposed framework by evaluating three state-of-the-art open-source LLMs (Llama, DeepSeek, Qwen) eliciting subgoals across various procedurally generated environment of the MiniGrid benchmark. Experimental results demonstrate that this curriculum-based approach accelerates learning and enhances exploration in complex tasks, achieving up to 30 to 200 times faster convergence in training steps compared to recent baselines designed for sparse reward environments.

Real-world robotic agents must act under partial observability and long horizons, where key cues may appear long before they affect decision making. However, most modern approaches rely solely on instantaneous information, without incorporating insights from the past. Standard recurrent or transformer models struggle with retaining and leveraging long-term dependencies: context windows truncate history, while naive memory extensions fail under scale and sparsity. We propose ELMUR (External Layer Memory with Update/Rewrite), a transformer architecture with structured external memory. Each layer maintains memory embeddings, interacts with them via bidirectional cross-attention, and updates them through an Least Recently Used (LRU) memory module using replacement or convex blending. ELMUR extends effective horizons up to 100,000 times beyond the attention window and achieves a 100% success rate on a synthetic T-Maze task with corridors up to one million steps. In POPGym, it outperforms baselines on more than half of the tasks. On MIKASA-Robo sparse-reward manipulation tasks with visual observations, it nearly doubles the performance of strong baselines. These results demonstrate that structured, layer-local external memory offers a simple and scalable approach to decision making under partial observability.

Nowadays transformer-based Large Language Models (LLM) for code generation tasks usually apply sampling and filtering pipelines. Due to the sparse reward problem in code generation tasks caused by one-token incorrectness, transformer-based models will sample redundant programs till they find a correct one, leading to low efficiency. To overcome the challenge, we incorporate Experience Replay (ER) in the fine-tuning phase, where codes and programs produced are stored and will be replayed to give the LLM agent a chance to learn from past experiences. Based on the spirit of ER, we introduce a novel approach called BTP pipeline which consists of three phases: beam search sampling, testing phase, and prioritized experience replay phase. The approach makes use of failed programs collected by code models and replays programs with high Possibility and Pass-rate Prioritized value (P2Value) from the replay buffer to improve efficiency. P2Value comprehensively considers the possibility of transformers' output and pass rate and can make use of the redundant resources caused by the problem that most programs collected by LLMs fail to pass any tests. We empirically apply our approach in several LLMs, demonstrating that it enhances their performance in code generation tasks and surpasses existing baselines.

One of the key challenges of Reinforcement Learning (RL) is the ability of agents to generalise their learned policy to unseen settings. Moreover, training RL agents requires large numbers of interactions with the environment. Motivated by the recent success of Offline RL and Imitation Learning (IL), we conduct a study to investigate whether agents can leverage offline data in the form of trajectories to improve the sample-efficiency in procedurally generated environments. We consider two settings of using IL from offline data for RL: (1) pre-training a policy before online RL training and (2) concurrently training a policy with online RL and IL from offline data. We analyse the impact of the quality (optimality of trajectories) and diversity (number of trajectories and covered level) of available offline trajectories on the effectiveness of both approaches. Across four well-known sparse reward tasks in the MiniGrid environment, we find that using IL for pre-training and concurrently during online RL training both consistently improve the sample-efficiency while converging to optimal policies. Furthermore, we show that pre-training a policy from as few as two trajectories can make the difference between learning an optimal policy at the end of online training and not learning at all. Our findings motivate the widespread adoption of IL for pre-training and concurrent IL in procedurally generated environments whenever offline trajectories are available or can be generated.

The role of reinforcement learning (RL) in enhancing the reasoning of large language models (LLMs) is becoming increasingly significant. Despite the success of RL in many scenarios, there are still many challenges in improving the reasoning of LLMs. One challenge is the sparse reward, which makes optimization difficult for RL and necessitates a large amount of data samples. Another challenge stems from the inherent instability of RL, particularly when using Actor-Critic (AC) methods to derive optimal policies, which often leads to unstable training processes. To address these issues, we introduce Direct Advantage Policy Optimization (DAPO), an novel step-level offline RL algorithm. Unlike standard alignment that rely solely outcome rewards to optimize policies (such as DPO), DAPO employs a critic function to predict the reasoning accuracy at each step, thereby generating dense signals to refine the generation strategy. Additionally, the Actor and Critic components in DAPO are trained independently, avoiding the co-training instability observed in standard AC algorithms like PPO. We train DAPO on mathematical and code query datasets and then evaluate its performance on multiple benchmarks. Our results show that DAPO can effectively enhance the mathematical and code capabilities on both SFT models and RL models, demonstrating the effectiveness of DAPO.

Recently, data augmentation (DA) has emerged as a method for leveraging domain knowledge to inexpensively generate additional data in reinforcement learning (RL) tasks, often yielding substantial improvements in data efficiency. While prior work has demonstrated the utility of incorporating augmented data directly into model-free RL updates, it is not well-understood when a particular DA strategy will improve data efficiency. In this paper, we seek to identify general aspects of DA responsible for observed learning improvements. Our study focuses on sparse-reward tasks with dynamics-invariant data augmentation functions, serving as an initial step towards a more general understanding of DA and its integration into RL training. Experimentally, we isolate three relevant aspects of DA: state-action coverage, reward density, and the number of augmented transitions generated per update (the augmented replay ratio). From our experiments, we draw two conclusions: (1) increasing state-action coverage often has a much greater impact on data efficiency than increasing reward density, and (2) decreasing the augmented replay ratio substantially improves data efficiency. In fact, certain tasks in our empirical study are solvable only when the replay ratio is sufficiently low.

Hierarchical reinforcement learning (RL) can accelerate long-horizon decision-making by temporally abstracting a policy into multiple levels. Promising results in sparse reward environments have been seen with skills, i.e. sequences of primitive actions. Typically, a skill latent space and policy are discovered from offline data, but the resulting low-level policy can be unreliable due to low-coverage demonstrations or distribution shifts. As a solution, we propose fine-tuning the low-level policy in conjunction with high-level skill selection. Our Skill-Critic algorithm optimizes both the low and high-level policies; these policies are also initialized and regularized by the latent space learned from offline demonstrations to guide the joint policy optimization. We validate our approach in multiple sparse RL environments, including a new sparse reward autonomous racing task in Gran Turismo Sport. The experiments show that Skill-Critic's low-level policy fine-tuning and demonstration-guided regularization are essential for optimal performance. Images and videos are available at https://sites.google.com/view/skill-critic. We plan to open source the code with the final version.

Diffusion models have emerged as powerful generative tools across various domains, yet tailoring pre-trained models to exhibit specific desirable properties remains challenging. While reinforcement learning (RL) offers a promising solution,current methods struggle to simultaneously achieve stable, efficient fine-tuning and support non-differentiable rewards. Furthermore, their reliance on sparse rewards provides inadequate supervision during intermediate steps, often resulting in suboptimal generation quality. To address these limitations, dense and differentiable signals are required throughout the diffusion process. Hence, we propose VAlue-based Reinforced Diffusion (VARD): a novel approach that first learns a value function predicting expection of rewards from intermediate states, and subsequently uses this value function with KL regularization to provide dense supervision throughout the generation process. Our method maintains proximity to the pretrained model while enabling effective and stable training via backpropagation. Experimental results demonstrate that our approach facilitates better trajectory guidance, improves training efficiency and extends the applicability of RL to diffusion models optimized for complex, non-differentiable reward functions.

Dealing with sparse rewards is one of the biggest challenges in Reinforcement Learning (RL). We present a novel technique called Hindsight Experience Replay which allows sample-efficient learning from rewards which are sparse and binary and therefore avoid the need for complicated reward engineering. It can be combined with an arbitrary off-policy RL algorithm and may be seen as a form of implicit curriculum. We demonstrate our approach on the task of manipulating objects with a robotic arm. In particular, we run experiments on three different tasks: pushing, sliding, and pick-and-place, in each case using only binary rewards indicating whether or not the task is completed. Our ablation studies show that Hindsight Experience Replay is a crucial ingredient which makes training possible in these challenging environments. We show that our policies trained on a physics simulation can be deployed on a physical robot and successfully complete the task.

In this paper, we propose R^3: Learning Reasoning through Reverse Curriculum Reinforcement Learning (RL), a novel method that employs only outcome supervision to achieve the benefits of process supervision for large language models. The core challenge in applying RL to complex reasoning is to identify a sequence of actions that result in positive rewards and provide appropriate supervision for optimization. Outcome supervision provides sparse rewards for final results without identifying error locations, whereas process supervision offers step-wise rewards but requires extensive manual annotation. R^3 overcomes these limitations by learning from correct demonstrations. Specifically, R^3 progressively slides the start state of reasoning from a demonstration's end to its beginning, facilitating easier model exploration at all stages. Thus, R^3 establishes a step-wise curriculum, allowing outcome supervision to offer step-level signals and precisely pinpoint errors. Using Llama2-7B, our method surpasses RL baseline on eight reasoning tasks by 4.1 points on average. Notebaly, in program-based reasoning on GSM8K, it exceeds the baseline by 4.2 points across three backbone models, and without any extra data, Codellama-7B + R^3 performs comparable to larger models or closed-source models.

We introduce AMAGO, an in-context Reinforcement Learning (RL) agent that uses sequence models to tackle the challenges of generalization, long-term memory, and meta-learning. Recent works have shown that off-policy learning can make in-context RL with recurrent policies viable. Nonetheless, these approaches require extensive tuning and limit scalability by creating key bottlenecks in agents' memory capacity, planning horizon, and model size. AMAGO revisits and redesigns the off-policy in-context approach to successfully train long-sequence Transformers over entire rollouts in parallel with end-to-end RL. Our agent is scalable and applicable to a wide range of problems, and we demonstrate its strong performance empirically in meta-RL and long-term memory domains. AMAGO's focus on sparse rewards and off-policy data also allows in-context learning to extend to goal-conditioned problems with challenging exploration. When combined with a multi-goal hindsight relabeling scheme, AMAGO can solve a previously difficult category of open-world domains, where agents complete many possible instructions in procedurally generated environments.

Performing Reinforcement Learning in sparse rewards settings, with very little prior knowledge, is a challenging problem since there is no signal to properly guide the learning process. In such situations, a good search strategy is fundamental. At the same time, not having to adapt the algorithm to every single problem is very desirable. Here we introduce TAXONS, a Task Agnostic eXploration of Outcome spaces through Novelty and Surprise algorithm. Based on a population-based divergent-search approach, it learns a set of diverse policies directly from high-dimensional observations, without any task-specific information. TAXONS builds a repertoire of policies while training an autoencoder on the high-dimensional observation of the final state of the system to build a low-dimensional outcome space. The learned outcome space, combined with the reconstruction error, is used to drive the search for new policies. Results show that TAXONS can find a diverse set of controllers, covering a good part of the ground-truth outcome space, while having no information about such space.

Training LLM agents in multi-turn environments with sparse rewards, where completing a single task requires 30+ turns of interaction within an episode, presents a fundamental challenge for reinforcement learning. We identify a critical failure mode unique to this setting: the exploration-exploitation cascade failure. This cascade begins with early-stage policy premature convergence, where sparse feedback causes agents to commit to flawed, low-entropy strategies. Subsequently, agents enter late-stage policy collapse, where conventional entropy regularization becomes counterproductive, promoting chaotic exploration that destabilizes training. We propose Entropy-regularized Policy Optimization (EPO), a general framework that breaks this failure cycle through three synergistic mechanisms: (1) adopting entropy regularization in multi-turn settings to enhance exploration, (2) an entropy smoothing regularizer that bounds policy entropy within historical averages to prevent abrupt fluctuations, and (3) adaptive phase-based weighting that balances exploration and exploitation across training. Our analysis justifies that EPO guarantees monotonically decreasing entropy variance while maintaining convergence. EPO achieves up to 152% performance improvement on ScienceWorld and up to 19.8% on ALFWorld. Our work demonstrates that multi-turn sparse-reward settings require fundamentally different entropy control than traditional RL, with broad implications for LLM agent training.

Language Models and Vision Language Models have recently demonstrated unprecedented capabilities in terms of understanding human intentions, reasoning, scene understanding, and planning-like behaviour, in text form, among many others. In this work, we investigate how to embed and leverage such abilities in Reinforcement Learning (RL) agents. We design a framework that uses language as the core reasoning tool, exploring how this enables an agent to tackle a series of fundamental RL challenges, such as efficient exploration, reusing experience data, scheduling skills, and learning from observations, which traditionally require separate, vertically designed algorithms. We test our method on a sparse-reward simulated robotic manipulation environment, where a robot needs to stack a set of objects. We demonstrate substantial performance improvements over baselines in exploration efficiency and ability to reuse data from offline datasets, and illustrate how to reuse learned skills to solve novel tasks or imitate videos of human experts.

While reinforcement learning (RL) shows remarkable success in decision-making problems, it often requires a lot of interactions with the environment, and in sparse-reward environments, it is challenging to learn meaningful policies. Large Language Models (LLMs) can potentially provide valuable guidance to agents in learning policies, thereby enhancing the performance of RL algorithms in such environments. However, LLMs often encounter difficulties in understanding downstream tasks, which hinders their ability to optimally assist agents in these tasks. A common approach to mitigating this issue is to fine-tune the LLMs with task-related data, enabling them to offer useful guidance for RL agents. However, this approach encounters several difficulties, such as inaccessible model weights or the need for significant computational resources, making it impractical. In this work, we introduce RLAdapter, a framework that builds a better connection between RL algorithms and LLMs by incorporating an adapter model. Within the RLAdapter framework, fine-tuning a lightweight language model with information generated during the training process of RL agents significantly aids LLMs in adapting to downstream tasks, thereby providing better guidance for RL agents. We conducted experiments to evaluate RLAdapter in the Crafter environment, and the results show that RLAdapter surpasses the SOTA baselines. Furthermore, agents under our framework exhibit common-sense behaviors that are absent in baseline models.

Learning to solve tasks from a sparse reward signal is a major challenge for standard reinforcement learning (RL) algorithms. However, in the real world, agents rarely need to solve sparse reward tasks entirely from scratch. More often, we might possess prior experience to draw on that provides considerable guidance about which actions and outcomes are possible in the world, which we can use to explore more effectively for new tasks. In this work, we study how prior data without reward labels may be used to guide and accelerate exploration for an agent solving a new sparse reward task. We propose a simple approach that learns a reward model from online experience, labels the unlabeled prior data with optimistic rewards, and then uses it concurrently alongside the online data for downstream policy and critic optimization. This general formula leads to rapid exploration in several challenging sparse-reward domains where tabula rasa exploration is insufficient, including the AntMaze domain, Adroit hand manipulation domain, and a visual simulated robotic manipulation domain. Our results highlight the ease of incorporating unlabeled prior data into existing online RL algorithms, and the (perhaps surprising) effectiveness of doing so.

Recent high-capacity vision-language-action (VLA) models have demonstrated impressive performance on a range of robotic manipulation tasks by imitating human demonstrations. However, exploiting offline data with limited visited states will cause execution failure in out-of-distribution scenarios. Intuitively, an exploration-based method that improves on online collected data at test time could address this limitation. We present VLA-RL, an algorithmic and systematic framework that leverages online reinforcement learning (RL) to improve pretrained auto-regressive VLAs in downstream tasks. Within a unified perspective, we first introduce a trajectory-level RL formulation for auto-regressive VLA training, which models general robotic manipulation trajectory as multi-modal multi-turn conversation. To address the challenge of sparse rewards, we fine-tune a pretrained vision-language model as a robotic process reward model, which is trained on pseudo reward labels annotated on automatically extracted task segments. To scale up, we identify several implementation findings that improve the stability and efficiency including curriculum selection strategy, GPU-balanced vectorized environments, batch decoding, and critic warmup. VLA-RL enables OpenVLA-7B to surpass the strongest finetuned baseline by 4.5% on 40 challenging robotic manipulation tasks in LIBERO, and even matches the performance of advanced commercial models such as pi_0-FAST. Notably, we observe that VLA-RL benefits from increased test-time optimization, indicating an early spark of inference scaling laws in robotics.

In recent years there have been remarkable advancements in autonomous driving. While autonomous vehicles demonstrate high performance in closed-set conditions, they encounter difficulties when confronted with unexpected situations. At the same time, world models emerged in the field of model-based reinforcement learning as a way to enable agents to predict the future depending on potential actions. This led to outstanding results in sparse reward and complex control tasks. This work provides an overview of how world models can be leveraged to perform anomaly detection in the domain of autonomous driving. We provide a characterization of world models and relate individual components to previous works in anomaly detection to facilitate further research in the field.

Reinforcement learning usually uses the feedback rewards of environmental to train agents. But the rewards in the actual environment are sparse, and even some environments will not rewards. Most of the current methods are difficult to get good performance in sparse reward or non-reward environments. Although using shaped rewards is effective when solving sparse reward tasks, it is limited to specific problems and learning is also susceptible to local optima. We propose a model-free method that does not rely on environmental rewards to solve the problem of sparse rewards in the general environment. Our method use the minimum number of transitions between states as the distance to replace the rewards of environmental, and proposes a goal-distance gradient to achieve policy improvement. We also introduce a bridge point planning method based on the characteristics of our method to improve exploration efficiency, thereby solving more complex tasks. Experiments show that our method performs better on sparse reward and local optimal problems in complex environments than previous work.

Robots have been successfully used to perform tasks with high precision. In real-world environments with sparse rewards and multiple goals, learning is still a major challenge and Reinforcement Learning (RL) algorithms fail to learn good policies. Training in simulation environments and then fine-tuning in the real world is a common approach. However, adapting to the real-world setting is a challenge. In this paper, we present a method named Ready for Production Hierarchical RL (ReProHRL) that divides tasks with hierarchical multi-goal navigation guided by reinforcement learning. We also use object detectors as a pre-processing step to learn multi-goal navigation and transfer it to the real world. Empirical results show that the proposed ReProHRL method outperforms the state-of-the-art baseline in simulation and real-world environments in terms of both training time and performance. Although both methods achieve a 100% success rate in a simple environment for single goal-based navigation, in a more complex environment and multi-goal setting, the proposed method outperforms the baseline by 18% and 5%, respectively. For the real-world implementation and proof of concept demonstration, we deploy the proposed method on a nano-drone named Crazyflie with a front camera to perform multi-goal navigation experiments.

A major challenge in Reinforcement Learning (RL) is the difficulty of learning an optimal policy from sparse rewards. Prior works enhance online RL with conventional Imitation Learning (IL) via a handcrafted auxiliary objective, at the cost of restricting the RL policy to be sub-optimal when the offline data is generated by a non-expert policy. Instead, to better leverage valuable information in offline data, we develop Generalized Imitation Learning from Demonstration (GILD), which meta-learns an objective that distills knowledge from offline data and instills intrinsic motivation towards the optimal policy. Distinct from prior works that are exclusive to a specific RL algorithm, GILD is a flexible module intended for diverse vanilla off-policy RL algorithms. In addition, GILD introduces no domain-specific hyperparameter and minimal increase in computational cost. In four challenging MuJoCo tasks with sparse rewards, we show that three RL algorithms enhanced with GILD significantly outperform state-of-the-art methods.

Intelligent agents need to select long sequences of actions to solve complex tasks. While humans easily break down tasks into subgoals and reach them through millions of muscle commands, current artificial intelligence is limited to tasks with horizons of a few hundred decisions, despite large compute budgets. Research on hierarchical reinforcement learning aims to overcome this limitation but has proven to be challenging, current methods rely on manually specified goal spaces or subtasks, and no general solution exists. We introduce Director, a practical method for learning hierarchical behaviors directly from pixels by planning inside the latent space of a learned world model. The high-level policy maximizes task and exploration rewards by selecting latent goals and the low-level policy learns to achieve the goals. Despite operating in latent space, the decisions are interpretable because the world model can decode goals into images for visualization. Director outperforms exploration methods on tasks with sparse rewards, including 3D maze traversal with a quadruped robot from an egocentric camera and proprioception, without access to the global position or top-down view that was used by prior work. Director also learns successful behaviors across a wide range of environments, including visual control, Atari games, and DMLab levels.

While current Multimodal Large Language Models (MLLMs) have demonstrated proficiency in reasoning tasks such as mathematics and logic, their capacity for long-chain reflective reasoning, a prerequisite for solving complex real-world problems, remains largely underexplored. In this work, we first conduct an extensive empirical investigation to evaluate this capability. Leveraging a carefully designed data synthesis engine, we construct MM-HELIX, a multimodal benchmark consisting 1,260 samples of 42 challenging synthetic tasks that require iterative thinking and backtracking. Empirical results on this benchmark reveal that existing MLLMs exhibit significant performance deficits in long-chain reflective reasoning. To address this limitation, we generate post-training data and further explore learning paradigms for exploiting such data. We first develop the Step-Elicited Response Generation pipeline to create MM-HELIX-100K, a large-scale dataset of 100k high-quality, reflective reasoning traces for instruction-tuning stage. Given that standard Reinforcement Learning fails on complex tasks due to sparse reward signals and catastrophic forgetting after Supervised Fine-Tuning, we propose Adaptive Hybrid Policy Optimization (AHPO), a novel training strategy that dynamically unifies offline supervision and online optimization into a single stage. This strategy enables the model to learn from expert data when rewards are sparse and conduct independent exploration once proficient. When applied to the Qwen2.5-VL-7B baseline, our method achieves a +18.6\% accuracy improvement on MM-HELIX benchmark and demonstrates strong generalization with a +5.7\% average performance gain on general mathematic and logic tasks. Our work demonstrate that reflective reasoning in MLLMs can be effectively learned and generalized, paving the way for developing more capable MLLMs.

Masked diffusion large language models (dLLMs) are emerging as promising alternatives to autoregressive LLMs, offering competitive performance while supporting unique generation capabilities such as inpainting. We explore how inpainting can inform RL algorithm design for dLLMs. Aligning LLMs with reinforcement learning faces an exploration challenge: sparse reward signals and sample waste when models fail to discover correct solutions. While this inefficiency affects LLMs broadly, dLLMs offer a distinctive opportunity--their inpainting ability can guide exploration. We introduce IGPO (Inpainting Guided Policy Optimization), an RL framework that strategically inserts partial ground-truth reasoning traces during online sampling. Unlike providing full solutions, inpainting steers exploration toward promising trajectory spaces while preserving self-generated reasoning, bridging supervised fine-tuning and reinforcement learning. We apply IGPO to group-based optimization methods such as GRPO, where exploration failures cause zero advantages and gradients. IGPO restores meaningful gradients while improving sample efficiency. We also propose supervised fine-tuning on synthetically rewritten concise traces that better align with dLLM generation patterns. With additional techniques including entropy-based filtering, our training recipe yields substantial gains across three mathematical benchmarks--GSM8K, Math500, and AMC--achieving new state-of-the-art results for full-attention masked dLLMs.

Latent diffusion models are the state-of-the-art for synthetic image generation. To align these models with human preferences, training the models using reinforcement learning on human feedback is crucial. Black et. al 2024 introduced denoising diffusion policy optimisation (DDPO), which accounts for the iterative denoising nature of the generation by modelling it as a Markov chain with a final reward. As the reward is a single value that determines the model's performance on the entire image, the model has to navigate a very sparse reward landscape and so requires a large sample count. In this work, we extend the DDPO by presenting the Pixel-wise Policy Optimisation (PXPO) algorithm, which can take feedback for each pixel, providing a more nuanced reward to the model.

In-context learning (ICL) is the ability of a model to learn a new task by observing a few exemplars in its context. While prevalent in NLP, this capability has recently also been observed in Reinforcement Learning (RL) settings. Prior in-context RL methods, however, require entire episodes in the agent's context. Given that complex environments typically lead to long episodes with sparse rewards, these methods are constrained to simple environments with short episodes. To address these challenges, we introduce Retrieval-Augmented Decision Transformer (RA-DT). RA-DT employs an external memory mechanism to store past experiences from which it retrieves only sub-trajectories relevant for the current situation. The retrieval component in RA-DT does not require training and can be entirely domain-agnostic. We evaluate the capabilities of RA-DT on grid-world environments, robotics simulations, and procedurally-generated video games. On grid-worlds, RA-DT outperforms baselines, while using only a fraction of their context length. Furthermore, we illuminate the limitations of current in-context RL methods on complex environments and discuss future directions. To facilitate future research, we release datasets for four of the considered environments.

Real-world sequential decision making is characterized by sparse rewards and large decision spaces, posing significant difficulty for experiential learning systems like tabula rasa reinforcement learning (RL) agents. Large Language Models (LLMs), with a wealth of world knowledge, can help RL agents learn quickly and adapt to distribution shifts. In this work, we introduce Language Guided Exploration (LGE) framework, which uses a pre-trained language model (called GUIDE ) to provide decision-level guidance to an RL agent (called EXPLORER). We observe that on ScienceWorld (Wang et al.,2022), a challenging text environment, LGE outperforms vanilla RL agents significantly and also outperforms other sophisticated methods like Behaviour Cloning and Text Decision Transformer.

The recent rapid advancement of machine learning has been driven by increasingly powerful models with the growing availability of training data and computational resources. However, real-time decision-making tasks with limited time and sparse learning signals remain challenging. One way of improving the learning speed and performance of these agents is to leverage human guidance. In this work, we introduce GUIDE, a framework for real-time human-guided reinforcement learning by enabling continuous human feedback and grounding such feedback into dense rewards to accelerate policy learning. Additionally, our method features a simulated feedback module that learns and replicates human feedback patterns in an online fashion, effectively reducing the need for human input while allowing continual training. We demonstrate the performance of our framework on challenging tasks with sparse rewards and visual observations. Our human study involving 50 subjects offers strong quantitative and qualitative evidence of the effectiveness of our approach. With only 10 minutes of human feedback, our algorithm achieves up to 30% increase in success rate compared to its RL baseline.

Offline reinforcement learning (RL) aims to find a near-optimal policy using pre-collected datasets. In real-world scenarios, data collection could be costly and risky; therefore, offline RL becomes particularly challenging when the in-domain data is limited. Given recent advances in Large Language Models (LLMs) and their few-shot learning prowess, this paper introduces Language Models for Motion Control (LaMo), a general framework based on Decision Transformers to effectively use pre-trained Language Models (LMs) for offline RL. Our framework highlights four crucial components: (1) Initializing Decision Transformers with sequentially pre-trained LMs, (2) employing the LoRA fine-tuning method, in contrast to full-weight fine-tuning, to combine the pre-trained knowledge from LMs and in-domain knowledge effectively, (3) using the non-linear MLP transformation instead of linear projections, to generate embeddings, and (4) integrating an auxiliary language prediction loss during fine-tuning to stabilize the LMs and retain their original abilities on languages. Empirical results indicate LaMo achieves state-of-the-art performance in sparse-reward tasks and closes the gap between value-based offline RL methods and decision transformers in dense-reward tasks. In particular, our method demonstrates superior performance in scenarios with limited data samples. Our project website is https://lamo2023.github.io

The outstanding capabilities of large language models (LLMs) render them a crucial component in various autonomous agent systems. While traditional methods depend on the inherent knowledge of LLMs without fine-tuning, more recent approaches have shifted toward the reinforcement learning strategy to further enhance agents' ability to solve complex interactive tasks with environments and tools. However, previous approaches are constrained by the sparse reward issue, where existing datasets solely provide a final scalar reward for each multi-step reasoning chain, potentially leading to ineffectiveness and inefficiency in policy learning. In this paper, we introduce StepAgent, which utilizes step-wise reward to optimize the agent's reinforcement learning process. Inheriting the spirit of novice-to-expert theory, we first compare the actions of the expert and the agent to automatically generate intermediate rewards for fine-grained optimization. Additionally, we propose implicit-reward and inverse reinforcement learning techniques to facilitate agent reflection and policy adjustment. Further theoretical analysis demonstrates that the action distribution of the agent can converge toward the expert action distribution over multiple training cycles. Experimental results across various datasets indicate that StepAgent outperforms existing baseline methods.

With the flourishing development of intelligent warehousing systems, the technology of Automated Guided Vehicle (AGV) has experienced rapid growth. Within intelligent warehousing environments, AGV is required to safely and rapidly plan an optimal path in complex and dynamic environments. Most research has studied deep reinforcement learning to address this challenge. However, in the environments with sparse extrinsic rewards, these algorithms often converge slowly, learn inefficiently or fail to reach the target. Random Network Distillation (RND), as an exploration enhancement, can effectively improve the performance of proximal policy optimization, especially enhancing the additional intrinsic rewards of the AGV agent which is in sparse reward environments. Moreover, most of the current research continues to use 2D grid mazes as experimental environments. These environments have insufficient complexity and limited action sets. To solve this limitation, we present simulation environments of AGV path planning with continuous actions and positions for AGVs, so that it can be close to realistic physical scenarios. Based on our experiments and comprehensive analysis of the proposed method, the results demonstrate that our proposed method enables AGV to more rapidly complete path planning tasks with continuous actions in our environments. A video of part of our experiments can be found at https://youtu.be/lwrY9YesGmw.

Reinforcement learning with verifiable reward (RLVR) has become a promising paradigm for post-training large language models (LLMs) to improve their reasoning capability. However, when the rollout accuracy is low on hard problems, the reward becomes sparse, limiting learning efficiency and causing exploration bottlenecks. Existing approaches either rely on teacher models for distillation or filter out difficult problems, which limits scalability or restricts reasoning improvement through exploration. We propose EvoCoT, a self-evolving curriculum learning framework based on two-stage chain-of-thought (CoT) reasoning optimization. EvoCoT constrains the exploration space by self-generating and verifying CoT trajectories, then gradually shortens CoT steps to expand the space in a controlled way. The framework enables LLMs to stably learn from initially unsolved hard problems under sparse rewards. We apply EvoCoT to multiple LLM families, including Qwen, DeepSeek, and Llama. Experiments show that EvoCoT enables LLMs to solve previously unsolved problems, improves reasoning capability without external CoT supervision, and is compatible with various RL fine-tuning methods. We release the source code to support future research.

In the era of Large Language Models (LLMs), alignment has emerged as a fundamental yet challenging problem in the pursuit of more reliable, controllable, and capable machine intelligence. The recent success of reasoning models and conversational AI systems has underscored the critical role of reinforcement learning (RL) in enhancing these systems, driving increased research interest at the intersection of RL and LLM alignment. This paper provides a comprehensive review of recent advances in LLM alignment through the lens of inverse reinforcement learning (IRL), emphasizing the distinctions between RL techniques employed in LLM alignment and those in conventional RL tasks. In particular, we highlight the necessity of constructing neural reward models from human data and discuss the formal and practical implications of this paradigm shift. We begin by introducing fundamental concepts in RL to provide a foundation for readers unfamiliar with the field. We then examine recent advances in this research agenda, discussing key challenges and opportunities in conducting IRL for LLM alignment. Beyond methodological considerations, we explore practical aspects, including datasets, benchmarks, evaluation metrics, infrastructure, and computationally efficient training and inference techniques. Finally, we draw insights from the literature on sparse-reward RL to identify open questions and potential research directions. By synthesizing findings from diverse studies, we aim to provide a structured and critical overview of the field, highlight unresolved challenges, and outline promising future directions for improving LLM alignment through RL and IRL techniques.

The Branch-and-bound (B&B) algorithm is the main solver for Mixed Integer Linear Programs (MILPs), where the selection of branching variable is essential to computational efficiency. However, traditional heuristics for branching often fail to generalize across heterogeneous problem instances, while existing learning-based methods such as imitation learning (IL) suffers from dependence on expert demonstration quality, and reinforcement learning (RL) struggles with limitations in sparse rewards and dynamic state representation challenges. To address these issues, we propose ReviBranch, a novel deep RL framework that constructs revived trajectories by reviving explicit historical correspondences between branching decisions and their corresponding graph states along search-tree paths. During training, ReviBranch enables agents to learn from complete structural evolution and temporal dependencies within the branching process. Additionally, we introduce an importance-weighted reward redistribution mechanism that transforms sparse terminal rewards into dense stepwise feedback, addressing the sparse reward challenge. Extensive experiments on different MILP benchmarks demonstrate that ReviBranch outperforms state-of-the-art RL methods, reducing B&B nodes by 4.0% and LP iterations by 2.2% on large-scale instances. The results highlight the robustness and generalizability of ReviBranch across heterogeneous MILP problem classes.

Chain-of-thought (CoT) reasoning is critical for improving the interpretability and reliability of Large Vision-Language Models (LVLMs). However, existing training algorithms such as SFT, PPO, and GRPO may not generalize well across unseen reasoning tasks and heavily rely on a biased reward model. To address this challenge, we reformulate reasoning in LVLMs as posterior inference and propose a scalable training algorithm based on amortized variational inference. By leveraging diversity-seeking reinforcement learning algorithms, we introduce a novel sparse reward function for token-level learning signals that encourage diverse, high-likelihood latent CoT, overcoming deterministic sampling limitations and avoiding reward hacking. Additionally, we implement a Bayesian inference-scaling strategy that replaces costly Best-of-N and Beam Search with a marginal likelihood to efficiently rank optimal rationales and answers. We empirically demonstrate that the proposed method enhances the state-of-the-art LVLMs on seven reasoning benchmarks, in terms of effectiveness, generalization, and interpretability.

While the field of Quality-Diversity (QD) has grown into a distinct branch of stochastic optimization, a few problems, in particular locomotion and navigation tasks, have become de facto standards. Are such benchmarks sufficient? Are they representative of the key challenges faced by QD algorithms? Do they provide the ability to focus on one particular challenge by properly disentangling it from others? Do they have much predictive power in terms of scalability and generalization? Existing benchmarks are not standardized, and there is currently no MNIST equivalent for QD. Inspired by recent works on Reinforcement Learning benchmarks, we argue that the identification of challenges faced by QD methods and the development of targeted, challenging, scalable but affordable benchmarks is an important step. As an initial effort, we identify three problems that are challenging in sparse reward settings, and propose associated benchmarks: (1) Behavior metric bias, which can result from the use of metrics that do not match the structure of the behavior space. (2) Behavioral Plateaus, with varying characteristics, such that escaping them would require adaptive QD algorithms and (3) Evolvability Traps, where small variations in genotype result in large behavioral changes. The environments that we propose satisfy the properties listed above.

The development of open benchmarking platforms could greatly accelerate the adoption of AI agents in retail. This paper presents comprehensive simulations of customer shopping behaviors for the purpose of benchmarking reinforcement learning (RL) agents that optimize coupon targeting. The difficulty of this learning problem is largely driven by the sparsity of customer purchase events. We trained agents using offline batch data comprising summarized customer purchase histories to help mitigate this effect. Our experiments revealed that contextual bandit and deep RL methods that are less prone to over-fitting the sparse reward distributions significantly outperform static policies. This study offers a practical framework for simulating AI agents that optimize the entire retail customer journey. It aims to inspire the further development of simulation tools for retail AI systems.

We investigate the challenge of parametrizing policies for reinforcement learning (RL) in high-dimensional continuous action spaces. Our objective is to develop a multimodal policy that overcomes limitations inherent in the commonly-used Gaussian parameterization. To achieve this, we propose a principled framework that models the continuous RL policy as a generative model of optimal trajectories. By conditioning the policy on a latent variable, we derive a novel variational bound as the optimization objective, which promotes exploration of the environment. We then present a practical model-based RL method, called Reparameterized Policy Gradient (RPG), which leverages the multimodal policy parameterization and learned world model to achieve strong exploration capabilities and high data efficiency. Empirical results demonstrate that our method can help agents evade local optima in tasks with dense rewards and solve challenging sparse-reward environments by incorporating an object-centric intrinsic reward. Our method consistently outperforms previous approaches across a range of tasks. Code and supplementary materials are available on the project page https://haosulab.github.io/RPG/

Poor sample efficiency continues to be the primary challenge for deployment of deep Reinforcement Learning (RL) algorithms for real-world applications, and in particular for visuo-motor control. Model-based RL has the potential to be highly sample efficient by concurrently learning a world model and using synthetic rollouts for planning and policy improvement. However, in practice, sample-efficient learning with model-based RL is bottlenecked by the exploration challenge. In this work, we find that leveraging just a handful of demonstrations can dramatically improve the sample-efficiency of model-based RL. Simply appending demonstrations to the interaction dataset, however, does not suffice. We identify key ingredients for leveraging demonstrations in model learning -- policy pretraining, targeted exploration, and oversampling of demonstration data -- which forms the three phases of our model-based RL framework. We empirically study three complex visuo-motor control domains and find that our method is 150%-250% more successful in completing sparse reward tasks compared to prior approaches in the low data regime (100K interaction steps, 5 demonstrations). Code and videos are available at: https://nicklashansen.github.io/modemrl

Online reinforcement learning in complex tasks is time-consuming, as massive interaction steps are needed to learn the optimal Q-function.Vision-language action (VLA) policies represent a promising direction for solving diverse tasks; however, their performance on low-level control remains limited, and effective deployment often requires task-specific expert demonstrations for fine-tuning. In this paper, we propose VARL (VLM as Action advisor for online Reinforcement Learning), a framework that leverages the domain knowledge of vision-language models (VLMs) to provide action suggestions for reinforcement learning agents. Unlike previous methods, VARL provides action suggestions rather than designing heuristic rewards, thereby guaranteeing unchanged optimality and convergence. The suggested actions increase sample diversity and ultimately improve sample efficiency, especially in sparse-reward tasks. To validate the effectiveness of VARL, we evaluate it across diverse environments and agent settings. Results show that VARL greatly improves sample efficiency without introducing significant computational overhead. These advantages make VARL a general framework for online reinforcement learning and make it feasible to directly apply reinforcement learning from scratch in real-world environments.

The Rubiks Cube, with its vast state space and sparse reward structure, presents a significant challenge for reinforcement learning (RL) due to the difficulty of reaching rewarded states. Previous research addressed this by propagating cost-to-go estimates from the solved state and incorporating search techniques. These approaches differ from human strategies that start from fully scrambled cubes, which can be tricky for solving a general sparse-reward problem. In this paper, we introduce a novel RL algorithm using policy gradient methods to solve the Rubiks Cube without relying on near solved-state sampling. Our approach employs a neural network to predict cost patterns between states, allowing the agent to learn directly from scrambled states. Our method was tested on the 2x2x2 Rubiks Cube, where the cube was scrambled 50,000 times, and the model successfully solved it in over 99.4% of cases. Notably, this result was achieved using only the policy network without relying on tree search as in previous methods, demonstrating its effectiveness and potential for broader applications in sparse-reward problems.

Offline Goal-Conditioned Reinforcement Learning (GCRL) is tasked with learning to achieve multiple goals in an environment purely from offline datasets using sparse reward functions. Offline GCRL is pivotal for developing generalist agents capable of leveraging pre-existing datasets to learn diverse and reusable skills without hand-engineering reward functions. However, contemporary approaches to GCRL based on supervised learning and contrastive learning are often suboptimal in the offline setting. An alternative perspective on GCRL optimizes for occupancy matching, but necessitates learning a discriminator, which subsequently serves as a pseudo-reward for downstream RL. Inaccuracies in the learned discriminator can cascade, negatively influencing the resulting policy. We present a novel approach to GCRL under a new lens of mixture-distribution matching, leading to our discriminator-free method: SMORe. The key insight is combining the occupancy matching perspective of GCRL with a convex dual formulation to derive a learning objective that can better leverage suboptimal offline data. SMORe learns scores or unnormalized densities representing the importance of taking an action at a state for reaching a particular goal. SMORe is principled and our extensive experiments on the fully offline GCRL benchmark composed of robot manipulation and locomotion tasks, including high-dimensional observations, show that SMORe can outperform state-of-the-art baselines by a significant margin.

Exploration bonuses in reinforcement learning guide long-horizon exploration by defining custom intrinsic objectives. Several exploration objectives like count-based bonuses, pseudo-counts, and state-entropy maximization are non-stationary and hence are difficult to optimize for the agent. While this issue is generally known, it is usually omitted and solutions remain under-explored. The key contribution of our work lies in transforming the original non-stationary rewards into stationary rewards through an augmented state representation. For this purpose, we introduce the Stationary Objectives For Exploration (SOFE) framework. SOFE requires identifying sufficient statistics for different exploration bonuses and finding an efficient encoding of these statistics to use as input to a deep network. SOFE is based on proposing state augmentations that expand the state space but hold the promise of simplifying the optimization of the agent's objective. We show that SOFE improves the performance of several exploration objectives, including count-based bonuses, pseudo-counts, and state-entropy maximization. Moreover, SOFE outperforms prior methods that attempt to stabilize the optimization of intrinsic objectives. We demonstrate the efficacy of SOFE in hard-exploration problems, including sparse-reward tasks, pixel-based observations, 3D navigation, and procedurally generated environments.

Model-based reinforcement learning (RL) algorithms designed for handling complex visual observations typically learn some sort of latent state representation, either explicitly or implicitly. Standard methods of this sort do not distinguish between functionally relevant aspects of the state and irrelevant distractors, instead aiming to represent all available information equally. We propose a modified objective for model-based RL that, in combination with mutual information maximization, allows us to learn representations and dynamics for visual model-based RL without reconstruction in a way that explicitly prioritizes functionally relevant factors. The key principle behind our design is to integrate a term inspired by variational empowerment into a state-space model based on mutual information. This term prioritizes information that is correlated with action, thus ensuring that functionally relevant factors are captured first. Furthermore, the same empowerment term also promotes faster exploration during the RL process, especially for sparse-reward tasks where the reward signal is insufficient to drive exploration in the early stages of learning. We evaluate the approach on a suite of vision-based robot control tasks with natural video backgrounds, and show that the proposed prioritized information objective outperforms state-of-the-art model based RL approaches with higher sample efficiency and episodic returns. https://sites.google.com/view/information-empowerment

Behavior cloning (BC) currently stands as a dominant paradigm for learning real-world visual manipulation. However, in tasks that require locally corrective behaviors like multi-part assembly, learning robust policies purely from human demonstrations remains challenging. Reinforcement learning (RL) can mitigate these limitations by allowing policies to acquire locally corrective behaviors through task reward supervision and exploration. This paper explores the use of RL fine-tuning to improve upon BC-trained policies in precise manipulation tasks. We analyze and overcome technical challenges associated with using RL to directly train policy networks that incorporate modern architectural components like diffusion models and action chunking. We propose training residual policies on top of frozen BC-trained diffusion models using standard policy gradient methods and sparse rewards, an approach we call ResiP (Residual for Precise manipulation). Our experimental results demonstrate that this residual learning framework can significantly improve success rates beyond the base BC-trained models in high-precision assembly tasks by learning corrective actions. We also show that by combining ResiP with teacher-student distillation and visual domain randomization, our method can enable learning real-world policies for robotic assembly directly from RGB images. Find videos and code at https://residual-assembly.github.io.

While AI agents have shown remarkable performance at various tasks, they still struggle with complex multi-modal applications, structured generation and strategic planning. Improvements via standard fine-tuning is often impractical, as solving agentic tasks usually relies on black box API access without control over model parameters. Inference-time methods such as Best-of-N (BON) sampling offer a simple yet effective alternative to improve performance. However, BON lacks iterative feedback integration mechanism. Hence, we propose Iterative Agent Decoding (IAD) which combines iterative refinement with dynamic candidate evaluation and selection guided by a verifier. IAD differs in how feedback is designed and integrated, specifically optimized to extract maximal signal from reward scores. We conduct a detailed comparison of baselines across key metrics on Sketch2Code, Text2SQL, and Webshop where IAD consistently outperforms baselines, achieving 3--6% absolute gains on Sketch2Code and Text2SQL (with and without LLM judges) and 8--10% gains on Webshop across multiple metrics. To better understand the source of IAD's gains, we perform controlled experiments to disentangle the effect of adaptive feedback from stochastic sampling, and find that IAD's improvements are primarily driven by verifier-guided refinement, not merely sampling diversity. We also show that both IAD and BON exhibit inference-time scaling with increased compute when guided by an optimal verifier. Our analysis highlights the critical role of verifier quality in effective inference-time optimization and examines the impact of noisy and sparse rewards on scaling behavior. Together, these findings offer key insights into the trade-offs and principles of effective inference-time optimization.

Unsupervised skill learning aims to learn a rich repertoire of behaviors without external supervision, providing artificial agents with the ability to control and influence the environment. However, without appropriate knowledge and exploration, skills may provide control only over a restricted area of the environment, limiting their applicability. Furthermore, it is unclear how to leverage the learned skill behaviors for adapting to downstream tasks in a data-efficient manner. We present Choreographer, a model-based agent that exploits its world model to learn and adapt skills in imagination. Our method decouples the exploration and skill learning processes, being able to discover skills in the latent state space of the model. During adaptation, the agent uses a meta-controller to evaluate and adapt the learned skills efficiently by deploying them in parallel in imagination. Choreographer is able to learn skills both from offline data, and by collecting data simultaneously with an exploration policy. The skills can be used to effectively adapt to downstream tasks, as we show in the URL benchmark, where we outperform previous approaches from both pixels and states inputs. The learned skills also explore the environment thoroughly, finding sparse rewards more frequently, as shown in goal-reaching tasks from the DMC Suite and Meta-World. Website and code: https://skillchoreographer.github.io/

Building agents capable of understanding language instructions is critical to effective and robust human-AI collaboration. Recent work focuses on training these agents via reinforcement learning in environments with synthetic language; however, instructions often define long-horizon, sparse-reward tasks, and learning policies requires many episodes of experience. We introduce ELLA: Exploration through Learned Language Abstraction, a reward shaping approach geared towards boosting sample efficiency in sparse reward environments by correlating high-level instructions with simpler low-level constituents. ELLA has two key elements: 1) A termination classifier that identifies when agents complete low-level instructions, and 2) A relevance classifier that correlates low-level instructions with success on high-level tasks. We learn the termination classifier offline from pairs of instructions and terminal states. Notably, in departure from prior work in language and abstraction, we learn the relevance classifier online, without relying on an explicit decomposition of high-level instructions to low-level instructions. On a suite of complex BabyAI environments with varying instruction complexities and reward sparsity, ELLA shows gains in sample efficiency relative to language-based shaping and traditional RL methods.

Learning in environments with large state and action spaces, and sparse rewards, can hinder a Reinforcement Learning (RL) agent's learning through trial-and-error. For instance, following natural language instructions on the Web (such as booking a flight ticket) leads to RL settings where input vocabulary and number of actionable elements on a page can grow very large. Even though recent approaches improve the success rate on relatively simple environments with the help of human demonstrations to guide the exploration, they still fail in environments where the set of possible instructions can reach millions. We approach the aforementioned problems from a different perspective and propose guided RL approaches that can generate unbounded amount of experience for an agent to learn from. Instead of learning from a complicated instruction with a large vocabulary, we decompose it into multiple sub-instructions and schedule a curriculum in which an agent is tasked with a gradually increasing subset of these relatively easier sub-instructions. In addition, when the expert demonstrations are not available, we propose a novel meta-learning framework that generates new instruction following tasks and trains the agent more effectively. We train DQN, deep reinforcement learning agent, with Q-value function approximated with a novel QWeb neural network architecture on these smaller, synthetic instructions. We evaluate the ability of our agent to generalize to new instructions on World of Bits benchmark, on forms with up to 100 elements, supporting 14 million possible instructions. The QWeb agent outperforms the baseline without using any human demonstration achieving 100% success rate on several difficult environments.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities across diverse tasks, yet they lag significantly behind humans in spatial reasoning. We investigate this gap through Transformation-Driven Visual Reasoning (TVR), a challenging task requiring identification of object transformations across images under varying viewpoints. While traditional Supervised Fine-Tuning (SFT) fails to generate coherent reasoning paths in cross-view settings, sparse-reward Reinforcement Learning (RL) suffers from inefficient exploration and slow convergence. To address these limitations, we propose STAR-R1, a novel framework that integrates a single-stage RL paradigm with a fine-grained reward mechanism tailored for TVR. Specifically, STAR-R1 rewards partial correctness while penalizing excessive enumeration and passive inaction, enabling efficient exploration and precise reasoning. Comprehensive evaluations demonstrate that STAR-R1 achieves state-of-the-art performance across all 11 metrics, outperforming SFT by 23% in cross-view scenarios. Further analysis reveals STAR-R1's anthropomorphic behavior and highlights its unique ability to compare all objects for improving spatial reasoning. Our work provides critical insights in advancing the research of MLLMs and reasoning models. The codes, model weights, and data will be publicly available at https://github.com/zongzhao23/STAR-R1.

The emergence of Multimodal Large Language Models (MLLMs) has driven significant advances in Graphical User Interface (GUI) agent capabilities. Nevertheless, existing GUI agent training and inference techniques still suffer from a dilemma for reasoning designs, ineffective reward, and visual noise. To address these issues, we introduce UI-AGILE, a comprehensive framework enhancing GUI agents at both the training and inference stages. For training, we propose a suite of improvements to the Supervised Fine-Tuning (SFT) process: 1) a Continuous Reward function to incentivize high-precision grounding; 2) a "Simple Thinking" reward to balance planning with speed and grounding accuracy; and 3) a Cropping-based Resampling strategy to mitigate the sparse reward problem and improve learning on complex tasks. For inference, we present Decomposed Grounding with Selection, a novel method that dramatically improves grounding accuracy on high-resolution displays by breaking the image into smaller, manageable parts. Experiments show that UI-AGILE achieves the state-of-the-art performance on two benchmarks ScreenSpot-Pro and ScreenSpot-v2. For instance, using both our proposed training and inference enhancement methods brings 23% grounding accuracy improvement over the best baseline on ScreenSpot-Pro.

Credit assignment, the process of attributing credit or blame to individual agents for their contributions to a team's success or failure, remains a fundamental challenge in multi-agent reinforcement learning (MARL), particularly in environments with sparse rewards. Commonly-used approaches such as value decomposition often lead to suboptimal policies in these settings, and designing dense reward functions that align with human intuition can be complex and labor-intensive. In this work, we propose a novel framework where a large language model (LLM) generates dense, agent-specific rewards based on a natural language description of the task and the overall team goal. By learning a potential-based reward function over multiple queries, our method reduces the impact of ranking errors while allowing the LLM to evaluate each agent's contribution to the overall task. Through extensive experiments, we demonstrate that our approach achieves faster convergence and higher policy returns compared to state-of-the-art MARL baselines.

Outcome-driven reinforcement learning has advanced reasoning in large language models (LLMs), but prevailing tool-augmented approaches train a single, monolithic policy that interleaves thoughts and tool calls under full context; this scales poorly with long horizons and diverse tools and generalizes weakly to new scenarios. Agentic systems offer a promising alternative by decomposing work across specialized modules, yet most remain training-free or rely on offline training decoupled from the live dynamics of multi-turn interaction. We introduce AgentFlow, a trainable, in-the-flow agentic framework that coordinates four modules (planner, executor, verifier, generator) through an evolving memory and directly optimizes its planner inside the multi-turn loop. To train on-policy in live environments, we propose Flow-based Group Refined Policy Optimization (Flow-GRPO), which tackles long-horizon, sparse-reward credit assignment by converting multi-turn optimization into a sequence of tractable single-turn policy updates. It broadcasts a single, verifiable trajectory-level outcome to every turn to align local planner decisions with global success and stabilizes learning with group-normalized advantages. Across ten benchmarks, AgentFlow with a 7B-scale backbone outperforms top-performing baselines with average accuracy gains of 14.9% on search, 14.0% on agentic, 14.5% on mathematical, and 4.1% on scientific tasks, even surpassing larger proprietary models like GPT-4o. Further analyses confirm the benefits of in-the-flow optimization, showing improved planning, enhanced tool-calling reliability, and positive scaling with model size and reasoning turns.

We present MiMo-7B, a large language model born for reasoning tasks, with optimization across both pre-training and post-training stages. During pre-training, we enhance the data preprocessing pipeline and employ a three-stage data mixing strategy to strengthen the base model's reasoning potential. MiMo-7B-Base is pre-trained on 25 trillion tokens, with additional Multi-Token Prediction objective for enhanced performance and accelerated inference speed. During post-training, we curate a dataset of 130K verifiable mathematics and programming problems for reinforcement learning, integrating a test-difficulty-driven code-reward scheme to alleviate sparse-reward issues and employing strategic data resampling to stabilize training. Extensive evaluations show that MiMo-7B-Base possesses exceptional reasoning potential, outperforming even much larger 32B models. The final RL-tuned model, MiMo-7B-RL, achieves superior performance on mathematics, code and general reasoning tasks, surpassing the performance of OpenAI o1-mini. The model checkpoints are available at https://github.com/xiaomimimo/MiMo.

Recent advances in embodied AI highlight the potential of vision language models (VLMs) as agents capable of perception, reasoning, and interaction in complex environments. However, top-performing systems rely on large-scale models that are costly to deploy, while smaller VLMs lack the necessary knowledge and skills to succeed. To bridge this gap, we present Embodied Reasoning Agent (ERA), a two-stage framework that integrates prior knowledge learning and online reinforcement learning (RL). The first stage, Embodied Prior Learning, distills foundational knowledge from three types of data: (1) Trajectory-Augmented Priors, which enrich existing trajectory data with structured reasoning generated by stronger models; (2) Environment-Anchored Priors, which provide in-environment knowledge and grounding supervision; and (3) External Knowledge Priors, which transfer general knowledge from out-of-environment datasets. In the second stage, we develop an online RL pipeline that builds on these priors to further enhance agent performance. To overcome the inherent challenges in agent RL, including long horizons, sparse rewards, and training instability, we introduce three key designs: self-summarization for context management, dense reward shaping, and turn-level policy optimization. Extensive experiments on both high-level planning (EB-ALFRED) and low-level control (EB-Manipulation) tasks demonstrate that ERA-3B surpasses both prompting-based large models and previous training-based baselines. Specifically, it achieves overall improvements of 8.4\% on EB-ALFRED and 19.4\% on EB-Manipulation over GPT-4o, and exhibits strong generalization to unseen tasks. Overall, ERA offers a practical path toward scalable embodied intelligence, providing methodological insights for future embodied AI systems.

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) have empowered large language models (LLMs) to tackle challenging reasoning tasks such as mathematics and programming. RLVR leverages verifiable outcome rewards to guide policy optimization, enabling LLMs to progressively improve output quality in a grounded and reliable manner. Despite its promise, the RLVR paradigm poses significant challenges, as existing methods often suffer from sparse reward signals and unstable policy gradient updates, particularly in RL-based approaches. To address the challenges, we propose PACS, a novel RLVR framework that achieves imPlicit Actor Critic coupling via a Supervised learning framework. By treating the outcome reward as a predictable label, we reformulate the RLVR problem into a supervised learning task over a score function parameterized by the policy model and optimized using cross-entropy loss. A detailed gradient analysis shows that this supervised formulation inherently recovers the classical policy gradient update while implicitly coupling actor and critic roles, yielding more stable and efficient training. Benchmarking on challenging mathematical reasoning tasks, PACS outperforms strong RLVR baselines, such as PPO and GRPO, achieving superior reasoning performance. For instance, PACS achieves 59.78\% at pass@256 on AIME 2025, representing improvements of 13.32 and 14.36 points over PPO and GRPO. This simple yet powerful framework offers a promising avenue for LLMs post-training with verifiable rewards. Our code and data are available as open source at https://github.com/ritzz-ai/PACS.

Reasoning language models such as OpenAI-o1, DeepSeek-R1, and Qwen achieve strong performance via extended chains of thought but often generate unnecessarily long outputs. Maximizing intelligence per token--accuracy relative to response length--remains an open problem. We revisit reinforcement learning (RL) with the simplest length penalty--truncation--and show that accuracy degradation arises not from the lack of sophisticated penalties but from inadequate RL optimization. We identify three key challenges: (i) large bias in advantage estimation, (ii) entropy collapse, and (iii) sparse reward signal. We address them with Doing Length pEnalty Right (DLER), a training recipe combining batch-wise reward normalization, higher clipping, dynamic sampling, and a simple truncation length penalty. DLER achieves state-of-the-art accuracy--efficiency trade-offs, cutting output length by over 70 percent while surpassing all previous baseline accuracy. It also improves test-time scaling: compared to DeepSeek-R1-7B, DLER-7B generates multiple concise responses in parallel with 28 percent higher accuracy and lower latency. We further introduce Difficulty-Aware DLER, which adaptively tightens truncation on easier questions for additional efficiency gains. We also propose an update-selective merging method that preserves baseline accuracy while retaining the concise reasoning ability of the DLER model, which is useful for scenarios where RL training data is scarce.

Recent progress, such as DeepSeek-R1, has shown that the GRPO algorithm, a Reinforcement Learning (RL) approach, can effectively train Chain-of-Thought (CoT) reasoning in Large Language Models (LLMs) and Vision-Language Models (VLMs). In this paper, we analyze three challenges of GRPO: gradient coupling between thoughts and answers, sparse reward signals caused by limited parallel sampling, and unstable advantage estimation. To mitigate these challenges, we propose GRPO-MA, a simple yet theoretically grounded method that leverages multi-answer generation from each thought process, enabling more robust and efficient optimization. Theoretically, we show that the variance of thought advantage decreases as the number of answers per thought increases. Empirically, our gradient analysis confirms this effect, showing that GRPO-MA reduces gradient spikes compared to GRPO. Experiments on math, code, and diverse multimodal tasks demonstrate that GRPO-MA substantially improves performance and training efficiency. Our ablation studies further reveal that increasing the number of answers per thought consistently enhances model performance.

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts Entropy-Driven Advantage and Guided Error Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.

Reinforcement learning (RL) is a critical component of large language model (LLM) post-training. However, existing on-policy algorithms used for post-training are inherently incompatible with the use of experience replay buffers, which can be populated scalably by distributed off-policy actors to enhance exploration as compute increases. We propose efficiently obtaining this benefit of replay buffers via Trajectory Balance with Asynchrony (TBA), a massively scalable LLM RL system. In contrast to existing approaches, TBA uses a larger fraction of compute on search, constantly generating off-policy data for a central replay buffer. A training node simultaneously samples data from this buffer based on reward or recency to update the policy using Trajectory Balance (TB), a diversity-seeking RL objective introduced for GFlowNets. TBA offers three key advantages: (1) decoupled training and search, speeding up training wall-clock time by 4x or more; (2) improved diversity through large-scale off-policy sampling; and (3) scalable search for sparse reward settings. On mathematical reasoning, preference-tuning, and automated red-teaming (diverse and representative post-training tasks), TBA produces speed and performance improvements over strong baselines.

Unsupervised pretraining has been transformative in many supervised domains. However, applying such ideas to reinforcement learning (RL) presents a unique challenge in that fine-tuning does not involve mimicking task-specific data, but rather exploring and locating the solution through iterative self-improvement. In this work, we study how unlabeled prior trajectory data can be leveraged to learn efficient exploration strategies. While prior data can be used to pretrain a set of low-level skills, or as additional off-policy data for online RL, it has been unclear how to combine these ideas effectively for online exploration. Our method SUPE (Skills from Unlabeled Prior data for Exploration) demonstrates that a careful combination of these ideas compounds their benefits. Our method first extracts low-level skills using a variational autoencoder (VAE), and then pseudo-relabels unlabeled trajectories using an optimistic reward model, transforming prior data into high-level, task-relevant examples. Finally, SUPE uses these transformed examples as additional off-policy data for online RL to learn a high-level policy that composes pretrained low-level skills to explore efficiently. We empirically show that SUPE reliably outperforms prior strategies, successfully solving a suite of long-horizon, sparse-reward tasks. Code: https://github.com/rail-berkeley/supe.

Learning control policies for complex, long-horizon tasks is a central challenge in robotics and autonomous systems. Signal Temporal Logic (STL) offers a powerful and expressive language for specifying such tasks, but its non-Markovian nature and inherent sparse reward make it difficult to be solved via standard Reinforcement Learning (RL) algorithms. Prior RL approaches focus only on limited STL fragments or use STL robustness scores as sparse terminal rewards. In this paper, we propose TGPO, Temporal Grounded Policy Optimization, to solve general STL tasks. TGPO decomposes STL into timed subgoals and invariant constraints and provides a hierarchical framework to tackle the problem. The high-level component of TGPO proposes concrete time allocations for these subgoals, and the low-level time-conditioned policy learns to achieve the sequenced subgoals using a dense, stage-wise reward signal. During inference, we sample various time allocations and select the most promising assignment for the policy network to rollout the solution trajectory. To foster efficient policy learning for complex STL with multiple subgoals, we leverage the learned critic to guide the high-level temporal search via Metropolis-Hastings sampling, focusing exploration on temporally feasible solutions. We conduct experiments on five environments, ranging from low-dimensional navigation to manipulation, drone, and quadrupedal locomotion. Under a wide range of STL tasks, TGPO significantly outperforms state-of-the-art baselines (especially for high-dimensional and long-horizon cases), with an average of 31.6% improvement in task success rate compared to the best baseline. The code will be available at https://github.com/mengyuest/TGPO

In this work, we aim to incentivize the reasoning ability of Multimodal Large Language Models (MLLMs) via reinforcement learning (RL) and develop an effective approach that mitigates the sparse reward and advantage vanishing issues during RL. To this end, we propose Share-GRPO, a novel RL approach that tackle these issues by exploring and sharing diverse reasoning trajectories over expanded question space. Specifically, Share-GRPO first expands the question space for a given question via data transformation techniques, and then encourages MLLM to effectively explore diverse reasoning trajectories over the expanded question space and shares the discovered reasoning trajectories across the expanded questions during RL. In addition, Share-GRPO also shares reward information during advantage computation, which estimates solution advantages hierarchically across and within question variants, allowing more accurate estimation of relative advantages and improving the stability of policy training. Extensive evaluations over six widely-used reasoning benchmarks showcase the superior performance of our method. Code will be available at https://github.com/HJYao00/R1-ShareVL.

In online reinforcement learning (online RL), balancing exploration and exploitation is crucial for finding an optimal policy in a sample-efficient way. To achieve this, existing sample-efficient online RL algorithms typically consist of three components: estimation, planning, and exploration. However, in order to cope with general function approximators, most of them involve impractical algorithmic components to incentivize exploration, such as optimization within data-dependent level-sets or complicated sampling procedures. To address this challenge, we propose an easy-to-implement RL framework called Maximize to Explore (MEX), which only needs to optimize unconstrainedly a single objective that integrates the estimation and planning components while balancing exploration and exploitation automatically. Theoretically, we prove that MEX achieves a sublinear regret with general function approximations for Markov decision processes (MDP) and is further extendable to two-player zero-sum Markov games (MG). Meanwhile, we adapt deep RL baselines to design practical versions of MEX, in both model-free and model-based manners, which can outperform baselines by a stable margin in various MuJoCo environments with sparse rewards. Compared with existing sample-efficient online RL algorithms with general function approximations, MEX achieves similar sample efficiency while enjoying a lower computational cost and is more compatible with modern deep RL methods.

The captivating realm of Minecraft has attracted substantial research interest in recent years, serving as a rich platform for developing intelligent agents capable of functioning in open-world environments. However, the current research landscape predominantly focuses on specific objectives, such as the popular "ObtainDiamond" task, and has not yet shown effective generalization to a broader spectrum of tasks. Furthermore, the current leading success rate for the "ObtainDiamond" task stands at around 20%, highlighting the limitations of Reinforcement Learning (RL) based controllers used in existing methods. To tackle these challenges, we introduce Ghost in the Minecraft (GITM), a novel framework integrates Large Language Models (LLMs) with text-based knowledge and memory, aiming to create Generally Capable Agents (GCAs) in Minecraft. These agents, equipped with the logic and common sense capabilities of LLMs, can skillfully navigate complex, sparse-reward environments with text-based interactions. We develop a set of structured actions and leverage LLMs to generate action plans for the agents to execute. The resulting LLM-based agent markedly surpasses previous methods, achieving a remarkable improvement of +47.5% in success rate on the "ObtainDiamond" task, demonstrating superior robustness compared to traditional RL-based controllers. Notably, our agent is the first to procure all items in the Minecraft Overworld technology tree, demonstrating its extensive capabilities. GITM does not need any GPU for training, but a single CPU node with 32 CPU cores is enough. This research shows the potential of LLMs in developing capable agents for handling long-horizon, complex tasks and adapting to uncertainties in open-world environments. See the project website at https://github.com/OpenGVLab/GITM.

Reinforcement learning (RL) is typically concerned with estimating stationary policies or single-step models, leveraging the Markov property to factorize problems in time. However, we can also view RL as a generic sequence modeling problem, with the goal being to produce a sequence of actions that leads to a sequence of high rewards. Viewed in this way, it is tempting to consider whether high-capacity sequence prediction models that work well in other domains, such as natural-language processing, can also provide effective solutions to the RL problem. To this end, we explore how RL can be tackled with the tools of sequence modeling, using a Transformer architecture to model distributions over trajectories and repurposing beam search as a planning algorithm. Framing RL as sequence modeling problem simplifies a range of design decisions, allowing us to dispense with many of the components common in offline RL algorithms. We demonstrate the flexibility of this approach across long-horizon dynamics prediction, imitation learning, goal-conditioned RL, and offline RL. Further, we show that this approach can be combined with existing model-free algorithms to yield a state-of-the-art planner in sparse-reward, long-horizon tasks.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for facilitating the self-improvement of large language models (LLMs), particularly in the domain of complex reasoning tasks. However, prevailing on-policy RL methods often contend with significant training instability and inefficiency. This is primarily due to a capacity-difficulty mismatch, where the complexity of training data frequently outpaces the model's current capabilities, leading to critically sparse reward signals and stalled learning progress. This challenge is particularly acute for smaller, more resource-efficient LLMs. To overcome this, we introduce the Guided Hybrid Policy Optimization (GHPO), a novel difficulty-aware reinforcement learning framework. GHPO dynamically calibrates task difficulty by employing adaptive prompt refinement to provide targeted guidance. This unique approach adaptively balances direct imitation learning for problems currently beyond the model's reach with exploration-based reinforcement learning for more manageable tasks, effectively creating a smooth and optimized learning curriculum. Extensive experiments demonstrate that GHPO achieves an average performance gain of approximately 5% across six challenging mathematics benchmarks, consistently outperforming strong on-policy reinforcement learning and curriculum learning baselines. Further analysis confirms that our framework significantly enhances both training stability and final reasoning performance, thus offering a scalable and efficient solution for developing powerful and robust reasoning models.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks, yet they face significant challenges in embodied task planning scenarios that require continuous environmental understanding and action generation. Existing approaches generate open-loop action scripts based on static knowledge, making it difficult to learn causal relationships between actions and environmental feedback, particularly in partially observable environments. We introduce Embodied Planner-R1, a novel outcome-driven reinforcement learning framework that enables LLMs to develop interactive capabilities through autonomous exploration with minimal supervision. Our framework incorporates three key innovations: (1) Without human annotations, we employ pure reinforcement learning with group rollout, incorporating in-environment interaction through parallel exploration; (2) completion-driven sparse reward; and (3) Interactive Policy Optimization (IPO) for efficient learning from grouped trajectories. Across two challenging text-based Embodied planning benchmarks, Embodied Planner-R1 achieves impressive completion rates of 97.78% on ALFWorld and 79.92% on ScienceWorld, surpassing prior methods by a large margin, and suffers only a -3.66% drop in previously unseen environments, evidencing strong generalization.

State-of-the-art (SOTA) reinforcement learning (RL) methods enable the vision-language agents to learn from interactions with the environment without human supervision. However, they struggle with learning inefficiencies in tackling real-world complex sequential decision-making tasks, especially with sparse reward signals and long-horizon dependencies. To effectively address the issue, we introduce Variational Subgoal-Conditioned RL (VSC-RL), which reformulates the vision-language sequential decision-making task as a variational goal-conditioned RL problem, allowing us to leverage advanced optimization methods to enhance learning efficiency. Specifically, VSC-RL optimizes the SubGoal Evidence Lower BOund (SGC-ELBO), which consists of (a) maximizing the subgoal-conditioned return via RL and (b) minimizing the subgoal-conditioned difference with the reference policy. We theoretically demonstrate that SGC-ELBO is equivalent to the original optimization objective, ensuring improved learning efficiency without sacrificing performance guarantees. Additionally, for real-world complex decision-making tasks, VSC-RL leverages the vision-language model to autonomously decompose the goal into feasible subgoals, enabling efficient learning. Across various benchmarks, including challenging real-world mobile device control tasks, VSC-RL significantly outperforms the SOTA vision-language agents, achieving superior performance and remarkable improvement in learning efficiency.

Offline reinforcement learning (RL) holds promise as a means to learn high-reward policies from a static dataset, without the need for further environment interactions. However, a key challenge in offline RL lies in effectively stitching portions of suboptimal trajectories from the static dataset while avoiding extrapolation errors arising due to a lack of support in the dataset. Existing approaches use conservative methods that are tricky to tune and struggle with multi-modal data (as we show) or rely on noisy Monte Carlo return-to-go samples for reward conditioning. In this work, we propose a novel approach that leverages the expressiveness of latent diffusion to model in-support trajectory sequences as compressed latent skills. This facilitates learning a Q-function while avoiding extrapolation error via batch-constraining. The latent space is also expressive and gracefully copes with multi-modal data. We show that the learned temporally-abstract latent space encodes richer task-specific information for offline RL tasks as compared to raw state-actions. This improves credit assignment and facilitates faster reward propagation during Q-learning. Our method demonstrates state-of-the-art performance on the D4RL benchmarks, particularly excelling in long-horizon, sparse-reward tasks.

Behavior Cloning (BC) on curated (or filtered) data is the predominant paradigm for supervised fine-tuning (SFT) of large language models; as well as for imitation learning of control policies. Here, we draw on a connection between this successful strategy and the theory and practice of finding optimal policies via Reinforcement Learning (RL). Building on existing literature, we clarify that SFT can be understood as maximizing a lower bound on the RL objective in a sparse reward setting. Giving support to its often observed good performance. From this viewpoint, we realize that a small modification to SFT leads to an importance weighted variant that behaves closer to training with RL as it: i) optimizes a tighter bound to the RL objective and, ii) can improve performance compared to SFT on curated data. We refer to this variant as importance weighted supervised fine-tuning (iw-SFT). We show that it is easy to implement and can be further generalized to training with quality scored data. The resulting SFT variants are competitive with more advanced RL algorithms for large language models and for training policies in continuous control tasks. For example achieving 66.7% on the AIME 2024 dataset.

While showing sophisticated reasoning abilities, large language models (LLMs) still struggle with long-horizon decision-making tasks due to deficient exploration and long-term credit assignment, especially in sparse-reward scenarios. Inspired by the divide-and-conquer principle, we propose an innovative framework **GLIDER** (**G**rounding **L**anguage Models as Eff**I**cient **D**ecision-Making Agents via Offline Hi**E**rarchical **R**einforcement Learning) that introduces a parameter-efficient and generally applicable hierarchy to LLM policies. We develop a scheme where the low-level controller is supervised with abstract, step-by-step plans that are learned and instructed by the high-level policy. This design decomposes complicated problems into a series of coherent chain-of-thought reasoning sub-tasks, providing flexible temporal abstraction to significantly enhance exploration and learning for long-horizon tasks. Furthermore, GLIDER facilitates fast online adaptation to non-stationary environments owing to the strong transferability of its task-agnostic low-level skills. Experiments on ScienceWorld and ALFWorld benchmarks show that GLIDER achieves consistent performance gains, along with enhanced generalization capabilities.

The VAPO framework has demonstrated significant empirical success in enhancing the efficiency and reliability of reinforcement learning for long chain-of-thought (CoT) reasoning tasks with large language models (LLMs). By systematically addressing challenges such as value model bias, heterogeneous sequence lengths, and sparse reward signals, VAPO achieves state-of-the-art performance. While its practical benefits are evident, a deeper theoretical understanding of its underlying mechanisms and potential limitations is crucial for guiding future advancements. This paper aims to initiate such a discussion by exploring VAPO from a theoretical perspective, highlighting areas where its assumptions might be challenged and where further investigation could yield more robust and generalizable reasoning agents. We delve into the intricacies of value function approximation in complex reasoning spaces, the optimality of adaptive advantage estimation, the impact of token-level optimization, and the enduring challenges of exploration and generalization.

Current Reinforcement Learning (RL) methods often suffer from sample-inefficiency, resulting from blind exploration strategies that neglect causal relationships among states, actions, and rewards. Although recent causal approaches aim to address this problem, they lack grounded modeling of reward-guided causal understanding of states and actions for goal-orientation, thus impairing learning efficiency. To tackle this issue, we propose a novel method named Causal Information Prioritization (CIP) that improves sample efficiency by leveraging factored MDPs to infer causal relationships between different dimensions of states and actions with respect to rewards, enabling the prioritization of causal information. Specifically, CIP identifies and leverages causal relationships between states and rewards to execute counterfactual data augmentation to prioritize high-impact state features under the causal understanding of the environments. Moreover, CIP integrates a causality-aware empowerment learning objective, which significantly enhances the agent's execution of reward-guided actions for more efficient exploration in complex environments. To fully assess the effectiveness of CIP, we conduct extensive experiments across 39 tasks in 5 diverse continuous control environments, encompassing both locomotion and manipulation skills learning with pixel-based and sparse reward settings. Experimental results demonstrate that CIP consistently outperforms existing RL methods across a wide range of scenarios.

Large Vision-Language Models (LVLMs) have demonstrated proficiency in tackling a variety of visual-language tasks. However, current LVLMs suffer from misalignment between text and image modalities which causes three kinds of hallucination problems, i.e., object existence, object attribute, and object relationship. To tackle this issue, existing methods mainly utilize Reinforcement Learning (RL) to align modalities in LVLMs. However, they still suffer from three main limitations: (1) General feedback can not indicate the hallucination type contained in the response; (2) Sparse rewards only give the sequence-level reward for the whole response; and (3)Annotation cost is time-consuming and labor-intensive. To handle these limitations, we propose an innovative method to align modalities in LVLMs through Fine-Grained Artificial Intelligence Feedback (FGAIF), which mainly consists of three steps: AI-based Feedback Collection, Fine-grained Reward Model Training, and Reinforcement Learning with Fine-grained Reward. Specifically, We first utilize AI tools to predict the types of hallucination for each segment in the response and obtain a collection of fine-grained feedback. Then, based on the collected reward data, three specialized reward models are trained to produce dense rewards. Finally, a novel fine-grained feedback module is integrated into the Proximal Policy Optimization (PPO) algorithm. Extensive experiments are conducted on hallucination and general benchmarks, demonstrating the superior performance of our proposed method. Notably, compared with previous models trained with the RL-based aligning method, our proposed method is effective even with fewer parameters.

In deep reinforcement learning (RL) research, there has been a concerted effort to design more efficient and productive exploration methods while solving sparse-reward problems. These exploration methods often share common principles (e.g., improving diversity) and implementation details (e.g., intrinsic reward). Prior work found that non-stationary Markov decision processes (MDPs) require exploration to efficiently adapt to changes in the environment with online transfer learning. However, the relationship between specific exploration characteristics and effective transfer learning in deep RL has not been characterized. In this work, we seek to understand the relationships between salient exploration characteristics and improved performance and efficiency in transfer learning. We test eleven popular exploration algorithms on a variety of transfer types -- or ``novelties'' -- to identify the characteristics that positively affect online transfer learning. Our analysis shows that some characteristics correlate with improved performance and efficiency across a wide range of transfer tasks, while others only improve transfer performance with respect to specific environment changes. From our analysis, make recommendations about which exploration algorithm characteristics are best suited to specific transfer situations.

While reinforcement learning (RL) has shown promising performance, its sample complexity continues to be a substantial hurdle, restricting its broader application across a variety of domains. Imitation learning (IL) utilizes oracles to improve sample efficiency, yet it is often constrained by the quality of the oracles deployed. which actively interleaves between IL and RL based on an online estimate of their performance. RPI draws on the strengths of IL, using oracle queries to facilitate exploration, an aspect that is notably challenging in sparse-reward RL, particularly during the early stages of learning. As learning unfolds, RPI gradually transitions to RL, effectively treating the learned policy as an improved oracle. This algorithm is capable of learning from and improving upon a diverse set of black-box oracles. Integral to RPI are Robust Active Policy Selection (RAPS) and Robust Policy Gradient (RPG), both of which reason over whether to perform state-wise imitation from the oracles or learn from its own value function when the learner's performance surpasses that of the oracles in a specific state. Empirical evaluations and theoretical analysis validate that RPI excels in comparison to existing state-of-the-art methodologies, demonstrating superior performance across various benchmark domains.

Offline reinforcement learning (RL) allows agents to learn effective, return-maximizing policies from a static dataset. Three popular algorithms for offline RL are Conservative Q-Learning (CQL), Behavior Cloning (BC), and Decision Transformer (DT), from the class of Q-Learning, Imitation Learning, and Sequence Modeling respectively. A key open question is: which algorithm is preferred under what conditions? We study this question empirically by exploring the performance of these algorithms across the commonly used D4RL and Robomimic benchmarks. We design targeted experiments to understand their behavior concerning data suboptimality, task complexity, and stochasticity. Our key findings are: (1) DT requires more data than CQL to learn competitive policies but is more robust; (2) DT is a substantially better choice than both CQL and BC in sparse-reward and low-quality data settings; (3) DT and BC are preferable as task horizon increases, or when data is obtained from human demonstrators; and (4) CQL excels in situations characterized by the combination of high stochasticity and low data quality. We also investigate architectural choices and scaling trends for DT on Atari and D4RL and make design/scaling recommendations. We find that scaling the amount of data for DT by 5x gives a 2.5x average score improvement on Atari.

Finding the optimal pass sequence of compilation can lead to a significant reduction in program size and/or improvement in program efficiency. Prior works on compilation pass ordering have two major drawbacks. They either require an excessive budget (in terms of compilation steps) at compile time or fail to generalize to unseen programs. In this paper, for code-size reduction tasks, we propose a novel pipeline to find program-dependent pass sequences within 45 compilation calls. It first identifies a coreset of 50 pass sequences via greedy optimization of a submodular function, and then learns a policy with Graph Neural Network (GNN) to pick the optimal sequence by predicting the normalized values of the pass sequences in the coreset. Despite its simplicity, our pipeline outperforms the default -Oz flag by an average of 4.7% over a large collection (4683) of unseen code repositories from diverse domains across 14 datasets. In comparison, previous approaches like reinforcement learning on the raw pass sequence space may take days to train due to sparse reward, and may not generalize well in held-out ones from different domains. Our results demonstrate that existing human-designed compiler flags can be improved with a simple yet effective technique that transforms the raw action space into a small one with denser rewards.

Automatic Curriculum Learning (ACL) has become a cornerstone of recent successes in Deep Reinforcement Learning (DRL).These methods shape the learning trajectories of agents by challenging them with tasks adapted to their capacities. In recent years, they have been used to improve sample efficiency and asymptotic performance, to organize exploration, to encourage generalization or to solve sparse reward problems, among others. The ambition of this work is dual: 1) to present a compact and accessible introduction to the Automatic Curriculum Learning literature and 2) to draw a bigger picture of the current state of the art in ACL to encourage the cross-breeding of existing concepts and the emergence of new ideas.

Deep artificial neural networks (DNNs) are typically trained via gradient-based learning algorithms, namely backpropagation. Evolution strategies (ES) can rival backprop-based algorithms such as Q-learning and policy gradients on challenging deep reinforcement learning (RL) problems. However, ES can be considered a gradient-based algorithm because it performs stochastic gradient descent via an operation similar to a finite-difference approximation of the gradient. That raises the question of whether non-gradient-based evolutionary algorithms can work at DNN scales. Here we demonstrate they can: we evolve the weights of a DNN with a simple, gradient-free, population-based genetic algorithm (GA) and it performs well on hard deep RL problems, including Atari and humanoid locomotion. The Deep GA successfully evolves networks with over four million free parameters, the largest neural networks ever evolved with a traditional evolutionary algorithm. These results (1) expand our sense of the scale at which GAs can operate, (2) suggest intriguingly that in some cases following the gradient is not the best choice for optimizing performance, and (3) make immediately available the multitude of neuroevolution techniques that improve performance. We demonstrate the latter by showing that combining DNNs with novelty search, which encourages exploration on tasks with deceptive or sparse reward functions, can solve a high-dimensional problem on which reward-maximizing algorithms (e.g.\ DQN, A3C, ES, and the GA) fail. Additionally, the Deep GA is faster than ES, A3C, and DQN (it can train Atari in {raise.17ex\scriptstyle\sim}4 hours on one desktop or {raise.17ex\scriptstyle\sim}1 hour distributed on 720 cores), and enables a state-of-the-art, up to 10,000-fold compact encoding technique.

Multi-agent reinforcement learning (MARL) demonstrates significant progress in solving cooperative and competitive multi-agent problems in various environments. One of the principal challenges in MARL is the need for explicit prediction of the agents' behavior to achieve cooperation. To resolve this issue, we propose the Shared Recurrent Memory Transformer (SRMT) which extends memory transformers to multi-agent settings by pooling and globally broadcasting individual working memories, enabling agents to exchange information implicitly and coordinate their actions. We evaluate SRMT on the Partially Observable Multi-Agent Pathfinding problem in a toy Bottleneck navigation task that requires agents to pass through a narrow corridor and on a POGEMA benchmark set of tasks. In the Bottleneck task, SRMT consistently outperforms a variety of reinforcement learning baselines, especially under sparse rewards, and generalizes effectively to longer corridors than those seen during training. On POGEMA maps, including Mazes, Random, and MovingAI, SRMT is competitive with recent MARL, hybrid, and planning-based algorithms. These results suggest that incorporating shared recurrent memory into the transformer-based architectures can enhance coordination in decentralized multi-agent systems. The source code for training and evaluation is available on GitHub: https://github.com/Aloriosa/srmt.

Recent advances in behavior cloning (BC) have enabled impressive visuomotor control policies. However, these approaches are limited by the quality of human demonstrations, the manual effort required for data collection, and the diminishing returns from increasing offline data. In comparison, reinforcement learning (RL) trains an agent through autonomous interaction with the environment and has shown remarkable success in various domains. Still, training RL policies directly on real-world robots remains challenging due to sample inefficiency, safety concerns, and the difficulty of learning from sparse rewards for long-horizon tasks, especially for high-degree-of-freedom (DoF) systems. We present a recipe that combines the benefits of BC and RL through a residual learning framework. Our approach leverages BC policies as black-box bases and learns lightweight per-step residual corrections via sample-efficient off-policy RL. We demonstrate that our method requires only sparse binary reward signals and can effectively improve manipulation policies on high-degree-of-freedom (DoF) systems in both simulation and the real world. In particular, we demonstrate, to the best of our knowledge, the first successful real-world RL training on a humanoid robot with dexterous hands. Our results demonstrate state-of-the-art performance in various vision-based tasks, pointing towards a practical pathway for deploying RL in the real world. Project website: https://residual-offpolicy-rl.github.io

Reasoning remains a challenging task for large language models (LLMs), especially within the logically constrained environment of automated theorem proving (ATP), due to sparse rewards and the vast scale of proofs. These challenges are amplified in benchmarks like PutnamBench, which contains university-level problems requiring complex, multi-step reasoning. To address this, we introduce self-generated goal-conditioned MDPs (sG-MDPs), a new framework in which agents generate and pursue their subgoals based on the evolving proof state. Given this more structured generation of goals, the resulting problem becomes more amenable to search. We then apply Monte Carlo Tree Search (MCTS)-like algorithms to solve the sG-MDP, instantiating our approach in Bourbaki (7B), a modular system that can ensemble multiple 7B LLMs for subgoal generation and tactic synthesis. On PutnamBench, Bourbaki (7B) solves 26 problems, achieving new state-of-the-art results with models at this scale.

Reinforcement Learning with Verifiable Reward (RLVR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due to its essentially on-policy strategy coupled with LLM's immense action space and sparse reward. Critically, RLVR can lead to the capability boundary collapse, narrowing the LLM's problem-solving scope. To address this problem, we propose RL-PLUS, a novel hybrid-policy optimization approach for LLMs that synergizes internal exploitation with external data to achieve stronger reasoning capabilities and surpass the boundaries of base models. RL-PLUS integrates two core components, i.e., Multiple Importance Sampling to address distributional mismatch from external data, and Exploration-Based Advantage Function to guide the model towards high-value, unexplored reasoning paths. We provide both theoretical analysis and extensive experiments to demonstrate the superiority and generalizability of our approach. Compared with existing RLVR methods, RL-PLUS achieves 1) state-of-the-art performance on six math reasoning benchmarks; 2) superior performance on six out-of-distribution reasoning tasks; 3) consistent and significant gains across diverse model families, with average relative improvements up to 69.2\%. Moreover, the analysis of Pass@k curves indicates that RL-PLUS effectively resolves the capability boundary collapse problem.

The pursuit of artificial agents that can learn to master complex environments has led to remarkable successes, yet prevailing deep reinforcement learning methods often rely on immense experience, encoding their knowledge opaquely within neural network weights. We propose a different paradigm, one in which an agent learns to play by reasoning and planning. We introduce Cogito, ergo ludo (CEL), a novel agent architecture that leverages a Large Language Model (LLM) to build an explicit, language-based understanding of its environment's mechanics and its own strategy. Starting from a tabula rasa state with no prior knowledge (except action set), CEL operates on a cycle of interaction and reflection. After each episode, the agent analyzes its complete trajectory to perform two concurrent learning processes: Rule Induction, where it refines its explicit model of the environment's dynamics, and Strategy and Playbook Summarization, where it distills experiences into an actionable strategic playbook. We evaluate CEL on diverse grid-world tasks (i.e., Minesweeper, Frozen Lake, and Sokoban), and show that the CEL agent successfully learns to master these games by autonomously discovering their rules and developing effective policies from sparse rewards. Ablation studies confirm that the iterative process is critical for sustained learning. Our work demonstrates a path toward more general and interpretable agents that not only act effectively but also build a transparent and improving model of their world through explicit reasoning on raw experience.

We propose ReinFlow, a simple yet effective online reinforcement learning (RL) framework that fine-tunes a family of flow matching policies for continuous robotic control. Derived from rigorous RL theory, ReinFlow injects learnable noise into a flow policy's deterministic path, converting the flow into a discrete-time Markov Process for exact and straightforward likelihood computation. This conversion facilitates exploration and ensures training stability, enabling ReinFlow to fine-tune diverse flow model variants, including Rectified Flow [35] and Shortcut Models [19], particularly at very few or even one denoising step. We benchmark ReinFlow in representative locomotion and manipulation tasks, including long-horizon planning with visual input and sparse reward. The episode reward of Rectified Flow policies obtained an average net growth of 135.36% after fine-tuning in challenging legged locomotion tasks while saving denoising steps and 82.63% of wall time compared to state-of-the-art diffusion RL fine-tuning method DPPO [43]. The success rate of the Shortcut Model policies in state and visual manipulation tasks achieved an average net increase of 40.34% after fine-tuning with ReinFlow at four or even one denoising step, whose performance is comparable to fine-tuned DDIM policies while saving computation time for an average of 23.20%. Project webpage: https://reinflow.github.io/

A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and finetuning them on correctly generated ones, performance quickly plateaus due to the scarcity of correct proofs (sparse rewards). To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises (which are often variants of known results) and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. The conjecturer is trained iteratively on previously generated conjectures that are barely provable by the current prover, which incentivizes it to generate increasingly challenging conjectures over time. The prover attempts to prove the conjectures with standard expert iteration. We evaluate STP with both Lean and Isabelle formal versifiers. With 19.8 billion tokens generated during the training in Lean, STP proves 26.3% of the statements in the LeanWorkbook dataset, doubling the previous best result of 13.2% achieved through expert iteration. The final model achieves state-of-the-art performance among whole-proof generation methods on miniF2F-test (61.7%, pass@3200), Proofnet-test (23.1%, pass@3200) and PutnamBench (8/644, pass@3200).

Reinforcement Learning has emerged as a post-training approach to elicit agentic RAG behaviors such as search and planning from language models. However, compact language models (e.g., 0.5B parameters) struggle due to poor reasoning ability, resulting in sparse rewards and unstable training. To overcome these difficulties, we propose Distillation-Guided Policy Optimization (DGPO), which addresses the challenges through cold-start initialization from teacher demonstrations and continuous teacher guidance during policy optimization. To systematically evaluate our approach, we introduce Agentic RAG Capabilities (ARC), a fine-grained metric analyzing reasoning, search coordination, and response synthesis. Comprehensive experiments demonstrate that DGPO enables compact models to achieve sophisticated agentic search behaviors, even outperforming the larger teacher model in some cases. DGPO makes agentic RAG feasible in computing resource-constrained environments.

A central challenge of the clean energy transition is the development of catalysts for low-emissions technologies. Recent advances in Machine Learning for quantum chemistry drastically accelerate the computation of catalytic activity descriptors such as adsorption energies. Here we introduce AdsorbRL, a Deep Reinforcement Learning agent aiming to identify potential catalysts given a multi-objective binding energy target, trained using offline learning on the Open Catalyst 2020 and Materials Project data sets. We experiment with Deep Q-Network agents to traverse the space of all ~160,000 possible unary, binary and ternary compounds of 55 chemical elements, with very sparse rewards based on adsorption energy known for only between 2,000 and 3,000 catalysts per adsorbate. To constrain the actions space, we introduce Random Edge Traversal and train a single-objective DQN agent on the known states subgraph, which we find strengthens target binding energy by an average of 4.1 eV. We extend this approach to multi-objective, goal-conditioned learning, and train a DQN agent to identify materials with the highest (respectively lowest) adsorption energies for multiple simultaneous target adsorbates. We experiment with Objective Sub-Sampling, a novel training scheme aimed at encouraging exploration in the multi-objective setup, and demonstrate simultaneous adsorption energy improvement across all target adsorbates, by an average of 0.8 eV. Overall, our results suggest strong potential for Deep Reinforcement Learning applied to the inverse catalysts design problem.

In this paper, we present the results of the NeurIPS-2022 Neural MMO Challenge, which attracted 500 participants and received over 1,600 submissions. Like the previous IJCAI-2022 Neural MMO Challenge, it involved agents from 16 populations surviving in procedurally generated worlds by collecting resources and defeating opponents. This year's competition runs on the latest v1.6 Neural MMO, which introduces new equipment, combat, trading, and a better scoring system. These elements combine to pose additional robustness and generalization challenges not present in previous competitions. This paper summarizes the design and results of the challenge, explores the potential of this environment as a benchmark for learning methods, and presents some practical reinforcement learning training approaches for complex tasks with sparse rewards. Additionally, we have open-sourced our baselines, including environment wrappers, benchmarks, and visualization tools for future research.

Reinforcement learning algorithms such as GRPO have driven recent advances in large language model (LLM) reasoning. While scaling the number of rollouts stabilizes training, existing approaches suffer from limited exploration on challenging prompts and leave informative feedback signals underexploited, due to context-independent rollout allocation across prompts (e.g., generating 16 rollouts per prompt) and relying heavily on sparse rewards. This paper presents XRPO(eXplore - eXploit GRPO), a unified framework that recasts policy optimization through the principled lens of rollout exploration-exploitation. To enhance exploration, XRPO introduces a mathematically grounded rollout allocator that adaptively prioritizes prompts with higher potential for uncertainty reduction. It further addresses stagnation on zero-reward prompts through an in-context seeding strategy that injects curated exemplars, steering the model into more difficult reasoning trajectories. To strengthen exploitation, XRPO develops a group-relative, novelty-aware advantage sharpening mechanism that leverages sequence likelihoods to amplify low-probability yet correct responses, thereby extending the policy's reach beyond sparse rewards. Experiments across diverse math and coding benchmarks on both reasoning and non-reasoning models demonstrate that XRPO outperforms existing advances (e.g., GRPO and GSPO) up to 4% pass@1 and 6% cons@32, while accelerating training convergence by up to 2.7X.

Training large language models (LLMs) as interactive agents for controlling graphical user interfaces (GUIs) presents a unique challenge to optimize long-horizon action sequences with multimodal feedback from complex environments. While recent works have advanced multi-turn reinforcement learning (RL) for reasoning and tool-using capabilities in LLMs, their application to GUI-based agents remains relatively underexplored due to the difficulty of sparse rewards, delayed feedback, and high rollout costs. In this paper, we investigate end-to-end policy optimization for vision-language-based GUI agents with the aim of improving performance on complex, long-horizon computer tasks. We propose Agentic Replay Policy Optimization (ARPO), an end-to-end RL approach that augments Group Relative Policy Optimization (GRPO) with a replay buffer to reuse the successful experience across training iterations. To further stabilize the training process, we propose a task selection strategy that filters tasks based on baseline agent performance, allowing the agent to focus on learning from informative interactions. Additionally, we compare ARPO with offline preference optimization approaches, highlighting the advantages of policy-based methods in GUI environments. Experiments on the OSWorld benchmark demonstrate that ARPO achieves competitive results, establishing a new performance baseline for LLM-based GUI agents trained via reinforcement learning. Our findings underscore the effectiveness of reinforcement learning for training multi-turn, vision-language GUI agents capable of managing complex real-world UI interactions. Codes and models:https://github.com/dvlab-research/ARPO.git.

Efficient multi-hop reasoning requires Large Language Models (LLMs) based agents to acquire high-value external knowledge iteratively. Previous work has explored reinforcement learning (RL) to train LLMs to perform search-based document retrieval, achieving notable improvements in QA performance, but underperform on complex, multi-hop QA resulting from the sparse rewards from global signal only. To address this gap in existing research, we introduce StepSearch, a framework for search LLMs that trained with step-wise proximal policy optimization method. It consists of richer and more detailed intermediate search rewards and token-level process supervision based on information gain and redundancy penalties to better guide each search step. We constructed a fine-grained question-answering dataset containing sub-question-level search trajectories based on open source datasets through a set of data pipeline method. On standard multi-hop QA benchmarks, it significantly outperforms global-reward baselines, achieving 11.2% and 4.2% absolute improvements for 3B and 7B models over various search with RL baselines using only 19k training data, demonstrating the effectiveness of fine-grained, stepwise supervision in optimizing deep search LLMs. Our code will be released on https://github.com/Zillwang/StepSearch.

The integration of reinforcement learning (RL) into the reasoning capabilities of Multimodal Large Language Models (MLLMs) has rapidly emerged as a transformative research direction. While MLLMs significantly extend Large Language Models (LLMs) to handle diverse modalities such as vision, audio, and video, enabling robust reasoning across multimodal inputs remains a major challenge. This survey systematically reviews recent advances in RL-based reasoning for MLLMs, covering key algorithmic designs, reward mechanism innovations, and practical applications. We highlight two main RL paradigms--value-free and value-based methods--and analyze how RL enhances reasoning abilities by optimizing reasoning trajectories and aligning multimodal information. Furthermore, we provide an extensive overview of benchmark datasets, evaluation protocols, and existing limitations, and propose future research directions to address current bottlenecks such as sparse rewards, inefficient cross-modal reasoning, and real-world deployment constraints. Our goal is to offer a comprehensive and structured guide to researchers interested in advancing RL-based reasoning in the multimodal era.

Diffusion models have revolutionized generative modeling in continuous domains like image, audio, and video synthesis. However, their iterative sampling process leads to slow generation and inefficient training, challenges that are further exacerbated when incorporating Reinforcement Learning from Human Feedback (RLHF) due to sparse rewards and long time horizons. Consistency models address these issues by enabling single-step or efficient multi-step generation, significantly reducing computational costs. In this work, we propose a direct reward optimization framework for applying RLHF to consistency models, incorporating distributional regularization to enhance training stability and prevent reward hacking. We investigate various f-divergences as regularization strategies, striking a balance between reward maximization and model consistency. Unlike policy gradient methods, our approach leverages first-order gradients, making it more efficient and less sensitive to hyperparameter tuning. Empirical results show that our method achieves competitive or superior performance compared to policy gradient based RLHF methods, across various automatic metrics and human evaluation. Additionally, our analysis demonstrates the impact of different regularization techniques in improving model generalization and preventing overfitting.

Long-horizon contact-rich tasks are challenging to learn with reinforcement learning, due to ineffective exploration of high-dimensional state spaces with sparse rewards. The learning process often gets stuck in local optimum and demands task-specific reward fine-tuning for complex scenarios. In this work, we propose a structured framework that leverages privileged actions with curriculum learning, enabling the policy to efficiently acquire long-horizon skills without relying on extensive reward engineering or reference trajectories. Specifically, we use privileged actions in simulation with a general training procedure that would be infeasible to implement in real-world scenarios. These privileges include relaxed constraints and virtual forces that enhance interaction and exploration with objects. Our results successfully achieve complex multi-stage long-horizon tasks that naturally combine non-prehensile manipulation with grasping to lift objects from non-graspable poses. We demonstrate generality by maintaining a parsimonious reward structure and showing convergence to diverse and robust behaviors across various environments. Additionally, real-world experiments further confirm that the skills acquired using our approach are transferable to real-world environments, exhibiting robust and intricate performance. Our approach outperforms state-of-the-art methods in these tasks, converging to solutions where others fail.

Efficient control in long-horizon robotic manipulation is challenging due to complex representation and policy learning requirements. Model-based visual reinforcement learning (RL) has shown great potential in addressing these challenges but still faces notable limitations, particularly in handling sparse rewards and complex visual features in long-horizon environments. To address these limitations, we propose the Recognize-Sense-Plan-Act (RSPA) pipeline for long-horizon tasks and further introduce RoboHorizon, an LLM-assisted multi-view world model tailored for long-horizon robotic manipulation. In RoboHorizon, pre-trained LLMs generate dense reward structures for multi-stage sub-tasks based on task language instructions, enabling robots to better recognize long-horizon tasks. Keyframe discovery is then integrated into the multi-view masked autoencoder (MAE) architecture to enhance the robot's ability to sense critical task sequences, strengthening its multi-stage perception of long-horizon processes. Leveraging these dense rewards and multi-view representations, a robotic world model is constructed to efficiently plan long-horizon tasks, enabling the robot to reliably act through RL algorithms. Experiments on two representative benchmarks, RLBench and FurnitureBench, show that RoboHorizon outperforms state-of-the-art visual model-based RL methods, achieving a 23.35% improvement in task success rates on RLBench's 4 short-horizon tasks and a 29.23% improvement on 6 long-horizon tasks from RLBench and 3 furniture assembly tasks from FurnitureBench.

Reinforcement Learning (RL) with unit test feedback has enhanced large language models (LLMs) code generation, but relies on sparse rewards provided only after complete code evaluation, limiting learning efficiency and incremental improvements. When generated code fails all unit tests, no learning signal is received, hindering progress on complex tasks. To address this, we propose a Process Reward Model (PRM) that delivers dense, line-level feedback on code correctness during generation, mimicking human code refinement and providing immediate guidance. We explore various strategies for training PRMs and integrating them into the RL framework, finding that using PRMs both as dense rewards and for value function initialization significantly boosts performance. Our approach increases our in-house LLM's pass rate from 28.2% to 29.8% on LiveCodeBench and from 31.8% to 35.8% on our internal benchmark. Our experimental results highlight the effectiveness of PRMs in enhancing RL-driven code generation, especially for long-horizon scenarios.

Representations are at the core of all deep reinforcement learning (RL) methods for both Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs). Many representation learning methods and theoretical frameworks have been developed to understand what constitutes an effective representation. However, the relationships between these methods and the shared properties among them remain unclear. In this paper, we show that many of these seemingly distinct methods and frameworks for state and history abstractions are, in fact, based on a common idea of self-predictive abstraction. Furthermore, we provide theoretical insights into the widely adopted objectives and optimization, such as the stop-gradient technique, in learning self-predictive representations. These findings together yield a minimalist algorithm to learn self-predictive representations for states and histories. We validate our theories by applying our algorithm to standard MDPs, MDPs with distractors, and POMDPs with sparse rewards. These findings culminate in a set of preliminary guidelines for RL practitioners.

Temporal abstraction and efficient planning pose significant challenges in offline reinforcement learning, mainly when dealing with domains that involve temporally extended tasks and delayed sparse rewards. Existing methods typically plan in the raw action space and can be inefficient and inflexible. Latent action spaces offer a more flexible paradigm, capturing only possible actions within the behavior policy support and decoupling the temporal structure between planning and modeling. However, current latent-action-based methods are limited to discrete spaces and require expensive planning. This paper presents a unified framework for continuous latent action space representation learning and planning by leveraging latent, score-based diffusion models. We establish the theoretical equivalence between planning in the latent action space and energy-guided sampling with a pretrained diffusion model and incorporate a novel sequence-level exact sampling method. Our proposed method, LatentDiffuser, demonstrates competitive performance on low-dimensional locomotion control tasks and surpasses existing methods in higher-dimensional tasks.

The MineRL competition is designed for the development of reinforcement learning and imitation learning algorithms that can efficiently leverage human demonstrations to drastically reduce the number of environment interactions needed to solve the complex ObtainDiamond task with sparse rewards. To address the challenge, in this paper, we present SEIHAI, a Sample-efficient Hierarchical AI, that fully takes advantage of the human demonstrations and the task structure. Specifically, we split the task into several sequentially dependent subtasks, and train a suitable agent for each subtask using reinforcement learning and imitation learning. We further design a scheduler to select different agents for different subtasks automatically. SEIHAI takes the first place in the preliminary and final of the NeurIPS-2020 MineRL competition.

RLCard is an open-source toolkit for reinforcement learning research in card games. It supports various card environments with easy-to-use interfaces, including Blackjack, Leduc Hold'em, Texas Hold'em, UNO, Dou Dizhu and Mahjong. The goal of RLCard is to bridge reinforcement learning and imperfect information games, and push forward the research of reinforcement learning in domains with multiple agents, large state and action space, and sparse reward. In this paper, we provide an overview of the key components in RLCard, a discussion of the design principles, a brief introduction of the interfaces, and comprehensive evaluations of the environments. The codes and documents are available at https://github.com/datamllab/rlcard

We introduce TextWorld, a sandbox learning environment for the training and evaluation of RL agents on text-based games. TextWorld is a Python library that handles interactive play-through of text games, as well as backend functions like state tracking and reward assignment. It comes with a curated list of games whose features and challenges we have analyzed. More significantly, it enables users to handcraft or automatically generate new games. Its generative mechanisms give precise control over the difficulty, scope, and language of constructed games, and can be used to relax challenges inherent to commercial text games like partial observability and sparse rewards. By generating sets of varied but similar games, TextWorld can also be used to study generalization and transfer learning. We cast text-based games in the Reinforcement Learning formalism, use our framework to develop a set of benchmark games, and evaluate several baseline agents on this set and the curated list.

Graphical User Interface (GUI) agents have demonstrated remarkable progress in automating complex user interface interactions through reinforcement learning. However, current approaches face a fundamental dilemma: offline RL enables stable training on pre-collected trajectories, but struggles with multi-step task execution for lack of trajectory-level reward signals; online RL captures these signals through environment interaction, but suffers from sparse rewards and prohibitive deployment costs. To address it, we present Semi-online Reinforcement Learning, a novel paradigm that simulates online RL on offline trajectories. During each rollout process, we preserve the original model output within the multi-turn dialogue, where a Patch Module adaptively recovers the divergence between rollout and expert trajectories. To capture long-term training signals, Semi-online RL introduces discounted future returns into the reward computation and optimizes the policy with weighted step-level and episode-level advantages. We further introduce Semi-Online Performance (SOP), a metric that aligns better with true online performance, serving as a practical and effective proxy for real-world evaluation. Experiments show that ours Semi-online RL achieves SOTA performance among 7B models across four dynamic benchmarks, with significant gains over the base model (e.g., +12.0% on AndroidWorld, +23.8% on AITW), demonstrating significant progress in bridging the gap between offline training efficiency and online multi-turn reasoning. The code is available at https://github.com/X-PLUG/MobileAgent/tree/main/UI-S1.

Improving the multi-step reasoning ability of large language models (LLMs) with offline reinforcement learning (RL) is essential for quickly adapting them to complex tasks. While Direct Preference Optimization (DPO) has shown promise in aligning LLMs with human preferences, it is less suitable for multi-step reasoning tasks because (1) DPO relies on paired preference data, which is not readily available for multi-step reasoning tasks, and (2) it treats all tokens uniformly, making it ineffective for credit assignment in multi-step reasoning tasks, which often come with sparse reward. In this work, we propose OREO (Offline Reasoning Optimization), an offline RL method for enhancing LLM multi-step reasoning. Building on insights from previous works of maximum entropy reinforcement learning, it jointly learns a policy model and value function by optimizing the soft Bellman Equation. We show in principle that it reduces the need to collect pairwise data and enables better credit assignment. Empirically, OREO surpasses existing offline learning methods on multi-step reasoning benchmarks, including mathematical reasoning tasks (GSM8K, MATH) and embodied agent control (ALFWorld). The approach can be extended to a multi-iteration framework when additional resources are available. Furthermore, the learned value function can be leveraged to guide the tree search for free, which can further boost performance during test time.

Being able to harness the power of large datasets for developing cooperative multi-agent controllers promises to unlock enormous value for real-world applications. Many important industrial systems are multi-agent in nature and are difficult to model using bespoke simulators. However, in industry, distributed processes can often be recorded during operation, and large quantities of demonstrative data stored. Offline multi-agent reinforcement learning (MARL) provides a promising paradigm for building effective decentralised controllers from such datasets. However, offline MARL is still in its infancy and therefore lacks standardised benchmark datasets and baselines typically found in more mature subfields of reinforcement learning (RL). These deficiencies make it difficult for the community to sensibly measure progress. In this work, we aim to fill this gap by releasing off-the-grid MARL (OG-MARL): a growing repository of high-quality datasets with baselines for cooperative offline MARL research. Our datasets provide settings that are characteristic of real-world systems, including complex environment dynamics, heterogeneous agents, non-stationarity, many agents, partial observability, suboptimality, sparse rewards and demonstrated coordination. For each setting, we provide a range of different dataset types (e.g. Good, Medium, Poor, and Replay) and profile the composition of experiences for each dataset. We hope that OG-MARL will serve the community as a reliable source of datasets and help drive progress, while also providing an accessible entry point for researchers new to the field.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

In the classical Reinforcement Learning from Human Feedback (RLHF) framework, Proximal Policy Optimization (PPO) is employed to learn from sparse, sentence-level rewards -- a challenging scenario in traditional deep reinforcement learning. Despite the great successes of PPO in the alignment of state-of-the-art closed-source large language models (LLMs), its open-source implementation is still largely sub-optimal, as widely reported by numerous research studies. To address these issues, we introduce a framework that models RLHF problems as a Markov decision process (MDP), enabling the capture of fine-grained token-wise information. Furthermore, we provide theoretical insights that demonstrate the superiority of our MDP framework over the previous sentence-level bandit formulation. Under this framework, we introduce an algorithm, dubbed as Reinforced Token Optimization (RTO), which learns the token-wise reward function from preference data and performs policy optimization based on this learned token-wise reward signal. Theoretically, RTO is proven to have the capability of finding the near-optimal policy sample-efficiently. For its practical implementation, RTO innovatively integrates Direct Preference Optimization (DPO) and PPO. DPO, originally derived from sparse sentence rewards, surprisingly provides us with a token-wise characterization of response quality, which is seamlessly incorporated into our subsequent PPO training stage. Extensive real-world alignment experiments verify the effectiveness of the proposed approach.

In many real-world scenarios, rewards extrinsic to the agent are extremely sparse, or absent altogether. In such cases, curiosity can serve as an intrinsic reward signal to enable the agent to explore its environment and learn skills that might be useful later in its life. We formulate curiosity as the error in an agent's ability to predict the consequence of its own actions in a visual feature space learned by a self-supervised inverse dynamics model. Our formulation scales to high-dimensional continuous state spaces like images, bypasses the difficulties of directly predicting pixels, and, critically, ignores the aspects of the environment that cannot affect the agent. The proposed approach is evaluated in two environments: VizDoom and Super Mario Bros. Three broad settings are investigated: 1) sparse extrinsic reward, where curiosity allows for far fewer interactions with the environment to reach the goal; 2) exploration with no extrinsic reward, where curiosity pushes the agent to explore more efficiently; and 3) generalization to unseen scenarios (e.g. new levels of the same game) where the knowledge gained from earlier experience helps the agent explore new places much faster than starting from scratch. Demo video and code available at https://pathak22.github.io/noreward-rl/

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

Recent flow matching models for text-to-image generation have achieved remarkable quality, yet their integration with reinforcement learning for human preference alignment remains suboptimal, hindering fine-grained reward-based optimization. We observe that the key impediment to effective GRPO training of flow models is the temporal uniformity assumption in existing approaches: sparse terminal rewards with uniform credit assignment fail to capture the varying criticality of decisions across generation timesteps, resulting in inefficient exploration and suboptimal convergence. To remedy this shortcoming, we introduce TempFlow-GRPO (Temporal Flow GRPO), a principled GRPO framework that captures and exploits the temporal structure inherent in flow-based generation. TempFlow-GRPO introduces two key innovations: (i) a trajectory branching mechanism that provides process rewards by concentrating stochasticity at designated branching points, enabling precise credit assignment without requiring specialized intermediate reward models; and (ii) a noise-aware weighting scheme that modulates policy optimization according to the intrinsic exploration potential of each timestep, prioritizing learning during high-impact early stages while ensuring stable refinement in later phases. These innovations endow the model with temporally-aware optimization that respects the underlying generative dynamics, leading to state-of-the-art performance in human preference alignment and standard text-to-image benchmarks.

Recent progress in aligning image and video generative models with Group Relative Policy Optimization (GRPO) has improved human preference alignment, but existing variants remain inefficient due to sequential rollouts and large numbers of sampling steps, unreliable credit assignment: sparse terminal rewards are uniformly propagated across timesteps, failing to capture the varying criticality of decisions during denoising. In this paper, we present BranchGRPO, a method that restructures the rollout process into a branching tree, where shared prefixes amortize computation and pruning removes low-value paths and redundant depths. BranchGRPO introduces three contributions: (1) a branching scheme that amortizes rollout cost through shared prefixes while preserving exploration diversity; (2) a reward fusion and depth-wise advantage estimator that transforms sparse terminal rewards into dense step-level signals; and (3) pruning strategies that cut gradient computation but leave forward rollouts and exploration unaffected. On HPDv2.1 image alignment, BranchGRPO improves alignment scores by up to 16\% over DanceGRPO, while reducing per-iteration training time by nearly 55\%. A hybrid variant, BranchGRPO-Mix, further accelerates training to 4.7x faster than DanceGRPO without degrading alignment. On WanX video generation, it further achieves higher Video-Align scores with sharper and temporally consistent frames compared to DanceGRPO. Codes are available at https://fredreic1849.github.io/BranchGRPO-Webpage/{BranchGRPO}.

Robotic systems that aspire to operate in uninstrumented real-world environments must perceive the world directly via onboard sensing. Vision-based learning systems aim to eliminate the need for environment instrumentation by building an implicit understanding of the world based on raw pixels, but navigating the contact-rich high-dimensional search space from solely sparse visual reward signals significantly exacerbates the challenge of exploration. The applicability of such systems is thus typically restricted to simulated or heavily engineered environments since agent exploration in the real-world without the guidance of explicit state estimation and dense rewards can lead to unsafe behavior and safety faults that are catastrophic. In this study, we isolate the root causes behind these limitations to develop a system, called MoDem-V2, capable of learning contact-rich manipulation directly in the uninstrumented real world. Building on the latest algorithmic advancements in model-based reinforcement learning (MBRL), demo-bootstrapping, and effective exploration, MoDem-V2 can acquire contact-rich dexterous manipulation skills directly in the real world. We identify key ingredients for leveraging demonstrations in model learning while respecting real-world safety considerations -- exploration centering, agency handover, and actor-critic ensembles. We empirically demonstrate the contribution of these ingredients in four complex visuo-motor manipulation problems in both simulation and the real world. To the best of our knowledge, our work presents the first successful system for demonstration-augmented visual MBRL trained directly in the real world. Visit https://sites.google.com/view/modem-v2 for videos and more details.

Large language models (LLMs) are increasingly adapted to downstream tasks via reinforcement learning (RL) methods like Group Relative Policy Optimization (GRPO), which often require thousands of rollouts to learn new tasks. We argue that the interpretable nature of language can often provide a much richer learning medium for LLMs, compared with policy gradients derived from sparse, scalar rewards. To test this, we introduce GEPA (Genetic-Pareto), a prompt optimizer that thoroughly incorporates natural language reflection to learn high-level rules from trial and error. Given any AI system containing one or more LLM prompts, GEPA samples system-level trajectories (e.g., reasoning, tool calls, and tool outputs) and reflects on them in natural language to diagnose problems, propose and test prompt updates, and combine complementary lessons from the Pareto frontier of its own attempts. As a result of GEPA's design, it can often turn even just a few rollouts into a large quality gain. Across four tasks, GEPA outperforms GRPO by 10% on average and by up to 20%, while using up to 35x fewer rollouts. GEPA also outperforms the leading prompt optimizer, MIPROv2, by over 10% across two LLMs, and demonstrates promising results as an inference-time search strategy for code optimization.

Reinforcement learning from human feedback (RLHF) has proven effective in aligning large language models (LLMs) with human preferences, but often at the cost of reduced output diversity. This trade-off between diversity and alignment quality remains a significant challenge. Drawing inspiration from curiosity-driven exploration in reinforcement learning, we introduce curiosity-driven RLHF (CD-RLHF), a framework that incorporates intrinsic rewards for novel states, alongside traditional sparse extrinsic rewards, to optimize both output diversity and alignment quality. We demonstrate the effectiveness of CD-RLHF through extensive experiments on a range of tasks, including text summarization and instruction following. Our approach achieves significant gains in diversity on multiple diversity-oriented metrics while maintaining alignment with human preferences comparable to standard RLHF. We make our code publicly available at https://github.com/ernie-research/CD-RLHF.

Large language models (LLMs) have been widely deployed across numerous fields. Reinforcement Learning from Human Feedback (RLHF) leverages reward models (RMs) as proxies for human preferences to align LLM behaviors with human values, making the accuracy, reliability, and interpretability of RMs critical for effective alignment. However, traditional RMs lack interpretability, offer limited insight into the reasoning behind reward assignments, and are inflexible toward user preference shifts. While recent multidimensional RMs aim for improved interpretability, they often fail to provide feature-level attribution and require costly annotations. To overcome these limitations, we introduce the Sparse Autoencoder-enhanced Reward Model (SARM), a novel architecture that integrates a pretrained Sparse Autoencoder (SAE) into a reward model. SARM maps the hidden activations of LLM-based RM into an interpretable, sparse, and monosemantic feature space, from which a scalar head aggregates feature activations to produce transparent and conceptually meaningful reward scores. Empirical evaluations demonstrate that SARM facilitates direct feature-level attribution of reward assignments, allows dynamic adjustment to preference shifts, and achieves superior alignment performance compared to conventional reward models. Our code is available at https://github.com/schrieffer-z/sarm.

Post-training for reasoning of large language models (LLMs) increasingly relies on verifiable rewards: deterministic checkers that provide 0-1 correctness signals. While reliable, such binary feedback is brittle--many tasks admit partially correct or alternative answers that verifiers under-credit, and the resulting all-or-nothing supervision limits learning. Reward models offer richer, continuous feedback, which can serve as a complementary supervisory signal to verifiers. We introduce HERO (Hybrid Ensemble Reward Optimization), a reinforcement learning framework that integrates verifier signals with reward-model scores in a structured way. HERO employs stratified normalization to bound reward-model scores within verifier-defined groups, preserving correctness while refining quality distinctions, and variance-aware weighting to emphasize challenging prompts where dense signals matter most. Across diverse mathematical reasoning benchmarks, HERO consistently outperforms RM-only and verifier-only baselines, with strong gains on both verifiable and hard-to-verify tasks. Our results show that hybrid reward design retains the stability of verifiers while leveraging the nuance of reward models to advance reasoning.

Dense process rewards have proven a more effective alternative to the sparse outcome-level rewards in the inference-time scaling of large language models (LLMs), particularly in tasks requiring complex multi-step reasoning. While dense rewards also offer an appealing choice for the reinforcement learning (RL) of LLMs since their fine-grained rewards have the potential to address some inherent issues of outcome rewards, such as training efficiency and credit assignment, this potential remains largely unrealized. This can be primarily attributed to the challenges of training process reward models (PRMs) online, where collecting high-quality process labels is prohibitively expensive, making them particularly vulnerable to reward hacking. To address these challenges, we propose PRIME (Process Reinforcement through IMplicit rEwards), which enables online PRM updates using only policy rollouts and outcome labels through implict process rewards. PRIME combines well with various advantage functions and forgoes the dedicated reward model training phrase that existing approaches require, substantially reducing the development overhead. We demonstrate PRIME's effectiveness on competitional math and coding. Starting from Qwen2.5-Math-7B-Base, PRIME achieves a 15.1% average improvement across several key reasoning benchmarks over the SFT model. Notably, our resulting model, Eurus-2-7B-PRIME, surpasses Qwen2.5-Math-7B-Instruct on seven reasoning benchmarks with 10% of its training data.

The integration of online reinforcement learning (RL) into diffusion and flow models has recently emerged as a promising approach for aligning generative models with human preferences. Stochastic sampling via Stochastic Differential Equations (SDE) is employed during the denoising process to generate diverse denoising directions for RL exploration. While existing methods effectively explore potential high-value samples, they suffer from sub-optimal preference alignment due to sparse and narrow reward signals. To address these challenges, we propose a novel Granular-GRPO (G^2RPO ) framework that achieves precise and comprehensive reward assessments of sampling directions in reinforcement learning of flow models. Specifically, a Singular Stochastic Sampling strategy is introduced to support step-wise stochastic exploration while enforcing a high correlation between the reward and the injected noise, thereby facilitating a faithful reward for each SDE perturbation. Concurrently, to eliminate the bias inherent in fixed-granularity denoising, we introduce a Multi-Granularity Advantage Integration module that aggregates advantages computed at multiple diffusion scales, producing a more comprehensive and robust evaluation of the sampling directions. Experiments conducted on various reward models, including both in-domain and out-of-domain evaluations, demonstrate that our G^2RPO significantly outperforms existing flow-based GRPO baselines,highlighting its effectiveness and robustness.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

The temporal credit assignment problem is a central challenge in Reinforcement Learning (RL), concerned with attributing the appropriate influence to each actions in a trajectory for their ability to achieve a goal. However, when feedback is delayed and sparse, the learning signal is poor, and action evaluation becomes harder. Canonical solutions, such as reward shaping and options, require extensive domain knowledge and manual intervention, limiting their scalability and applicability. In this work, we lay the foundations for Credit Assignment with Language Models (CALM), a novel approach that leverages Large Language Models (LLMs) to automate credit assignment via reward shaping and options discovery. CALM uses LLMs to decompose a task into elementary subgoals and assess the achievement of these subgoals in state-action transitions. Every time an option terminates, a subgoal is achieved, and CALM provides an auxiliary reward. This additional reward signal can enhance the learning process when the task reward is sparse and delayed without the need for human-designed rewards. We provide a preliminary evaluation of CALM using a dataset of human-annotated demonstrations from MiniHack, suggesting that LLMs can be effective in assigning credit in zero-shot settings, without examples or LLM fine-tuning. Our preliminary results indicate that the knowledge of LLMs is a promising prior for credit assignment in RL, facilitating the transfer of human knowledge into value functions.

Recent advancements in code generation have shown remarkable success across software domains, yet hardware description languages (HDLs) such as Verilog remain underexplored due to their concurrency semantics, syntactic rigidity, and simulation complexity. In this work, we address these challenges by introducing a reinforcement learning (RL) framework tailored for Verilog code generation. We first construct Veribench-53K, a high-quality dataset curated from over 700K Verilog problems, enriched with structured prompts, complexity labels, and diverse testbenches. To tackle the problem of sparse and noisy reward signals, we propose a Trace-back based Rescore mechanism that leverages reasoning paths and iterative refinement to enhance feedback reliability and support reward model training. Furthermore, to mitigate catastrophic forgetting and overfitting during RL fine-tuning, we introduce a sample-balanced weighting strategy that adaptively balances learning dynamics based on reward-probability distributions. These innovations are integrated into an iterative RL pipeline that co-evolves the policy and reward models. In contrast to recent work such as CraftRTL, which relies on large-scale closed-source model distillation, and DeepSeek-style approaches that struggle with sparse feedback, our method demonstrates superior performance using a smaller but high-quality dataset combined with RL optimization. Experiments on Verilog generation tasks demonstrate state-of-the-art performance, with substantial gains in test pass rate, functional correctness, and compilation robustness. Our findings highlight the potential of RL-driven approaches for structured code generation in hardware-centric domains. VERIRL is publicly available at https://github.com/omniAI-Lab/VeriRL.

Training reinforcement learning (RL) agents on robotic tasks typically requires a large number of training samples. This is because training data often consists of noisy trajectories, whether from exploration or human-collected demonstrations, making it difficult to learn value functions that understand the effect of taking each action. On the other hand, recent behavior-cloning (BC) approaches have shown that predicting a sequence of actions enables policies to effectively approximate noisy, multi-modal distributions of expert demonstrations. Can we use a similar idea for improving RL on robotic tasks? In this paper, we introduce a novel RL algorithm that learns a critic network that outputs Q-values over a sequence of actions. By explicitly training the value functions to learn the consequence of executing a series of current and future actions, our algorithm allows for learning useful value functions from noisy trajectories. We study our algorithm across various setups with sparse and dense rewards, and with or without demonstrations, spanning mobile bi-manual manipulation, whole-body control, and tabletop manipulation tasks from BiGym, HumanoidBench, and RLBench. We find that, by learning the critic network with action sequences, our algorithm outperforms various RL and BC baselines, in particular on challenging humanoid control tasks.

A grand challenge in reinforcement learning is intelligent exploration, especially when rewards are sparse or deceptive. Two Atari games serve as benchmarks for such hard-exploration domains: Montezuma's Revenge and Pitfall. On both games, current RL algorithms perform poorly, even those with intrinsic motivation, which is the dominant method to improve performance on hard-exploration domains. To address this shortfall, we introduce a new algorithm called Go-Explore. It exploits the following principles: (1) remember previously visited states, (2) first return to a promising state (without exploration), then explore from it, and (3) solve simulated environments through any available means (including by introducing determinism), then robustify via imitation learning. The combined effect of these principles is a dramatic performance improvement on hard-exploration problems. On Montezuma's Revenge, Go-Explore scores a mean of over 43k points, almost 4 times the previous state of the art. Go-Explore can also harness human-provided domain knowledge and, when augmented with it, scores a mean of over 650k points on Montezuma's Revenge. Its max performance of nearly 18 million surpasses the human world record, meeting even the strictest definition of "superhuman" performance. On Pitfall, Go-Explore with domain knowledge is the first algorithm to score above zero. Its mean score of almost 60k points exceeds expert human performance. Because Go-Explore produces high-performing demonstrations automatically and cheaply, it also outperforms imitation learning work where humans provide solution demonstrations. Go-Explore opens up many new research directions into improving it and weaving its insights into current RL algorithms. It may also enable progress on previously unsolvable hard-exploration problems in many domains, especially those that harness a simulator during training (e.g. robotics).

A generally intelligent agent must be able to teach itself how to solve problems in complex domains with minimal human supervision. Recently, deep reinforcement learning algorithms combined with self-play have achieved superhuman proficiency in Go, Chess, and Shogi without human data or domain knowledge. In these environments, a reward is always received at the end of the game, however, for many combinatorial optimization environments, rewards are sparse and episodes are not guaranteed to terminate. We introduce Autodidactic Iteration: a novel reinforcement learning algorithm that is able to teach itself how to solve the Rubik's Cube with no human assistance. Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves -- less than or equal to solvers that employ human domain knowledge.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Reinforcement learning (RL) agents improve through trial-and-error, but when reward is sparse and the agent cannot discover successful action sequences, learning stagnates. This has been a notable problem in training deep RL agents to perform web-based tasks, such as booking flights or replying to emails, where a single mistake can ruin the entire sequence of actions. A common remedy is to "warm-start" the agent by pre-training it to mimic expert demonstrations, but this is prone to overfitting. Instead, we propose to constrain exploration using demonstrations. From each demonstration, we induce high-level "workflows" which constrain the allowable actions at each time step to be similar to those in the demonstration (e.g., "Step 1: click on a textbox; Step 2: enter some text"). Our exploration policy then learns to identify successful workflows and samples actions that satisfy these workflows. Workflows prune out bad exploration directions and accelerate the agent's ability to discover rewards. We use our approach to train a novel neural policy designed to handle the semi-structured nature of websites, and evaluate on a suite of web tasks, including the recent World of Bits benchmark. We achieve new state-of-the-art results, and show that workflow-guided exploration improves sample efficiency over behavioral cloning by more than 100x.

In multi-goal Reinforcement Learning, an agent can share experience between related training tasks, resulting in better generalization for new tasks at test time. However, when the goal space has discontinuities and the reward is sparse, a majority of goals are difficult to reach. In this context, a curriculum over goals helps agents learn by adapting training tasks to their current capabilities. In this work we propose Stein Variational Goal Generation (SVGG), which samples goals of intermediate difficulty for the agent, by leveraging a learned predictive model of its goal reaching capabilities. The distribution of goals is modeled with particles that are attracted in areas of appropriate difficulty using Stein Variational Gradient Descent. We show that SVGG outperforms state-of-the-art multi-goal Reinforcement Learning methods in terms of success coverage in hard exploration problems, and demonstrate that it is endowed with a useful recovery property when the environment changes.

Recent advances in group-based reinforcement learning (RL) have driven frontier large language models (LLMs) in single-turn tasks like mathematical reasoning. However, their scalability to long-horizon LLM agent training remains limited. Unlike static tasks, agent-environment interactions unfold over many steps and often yield sparse or delayed rewards, making credit assignment across individual steps significantly more challenging. In this work, we propose Group-in-Group Policy Optimization (GiGPO), a novel RL algorithm that achieves fine-grained credit assignment for LLM agents while preserving the appealing properties of group-based RL: critic-free, low memory, and stable convergence. GiGPO introduces a two-level structure for estimating relative advantage: (i) At the episode-level, GiGPO computes macro relative advantages based on groups of complete trajectories; (ii) At the step-level, GiGPO introduces an anchor state grouping mechanism that retroactively constructs step-level groups by identifying repeated environment states across trajectories. Actions stemming from the same state are grouped together, enabling micro relative advantage estimation. This hierarchical structure effectively captures both global trajectory quality and local step effectiveness without relying on auxiliary models or additional rollouts. We evaluate GiGPO on two challenging agent benchmarks, ALFWorld and WebShop, using Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct. Crucially, GiGPO delivers fine-grained per-step credit signals and achieves performance gains of > 12\% on ALFWorld and > 9\% on WebShop over the GRPO baseline: all while maintaining the same GPU memory overhead, identical LLM rollout, and incurring little to no additional time cost.

We introduce RIPT-VLA, a simple and scalable reinforcement-learning-based interactive post-training paradigm that fine-tunes pretrained Vision-Language-Action (VLA) models using only sparse binary success rewards. Existing VLA training pipelines rely heavily on offline expert demonstration data and supervised imitation, limiting their ability to adapt to new tasks and environments under low-data regimes. RIPT-VLA addresses this by enabling interactive post-training with a stable policy optimization algorithm based on dynamic rollout sampling and leave-one-out advantage estimation. RIPT-VLA has the following characteristics. First, it applies to various VLA models, resulting in an improvement on the lightweight QueST model by 21.2%, and the 7B OpenVLA-OFT model to an unprecedented 97.5% success rate. Second, it is computationally efficient and data-efficient: with only one demonstration, RIPT-VLA enables an unworkable SFT model (4%) to succeed with a 97% success rate within 15 iterations. Furthermore, we demonstrate that the policy learned by RIPT-VLA generalizes across different tasks and scenarios and is robust to the initial state context. These results highlight RIPT-VLA as a practical and effective paradigm for post-training VLA models through minimal supervision.

Unsupervised goal-conditioned reinforcement learning (GCRL) is a promising paradigm for developing diverse robotic skills without external supervision. However, existing unsupervised GCRL methods often struggle to cover a wide range of states in complex environments due to their limited exploration and sparse or noisy rewards for GCRL. To overcome these challenges, we propose a novel unsupervised GCRL method that leverages TemporaL Distance-aware Representations (TLDR). TLDR selects faraway goals to initiate exploration and computes intrinsic exploration rewards and goal-reaching rewards, based on temporal distance. Specifically, our exploration policy seeks states with large temporal distances (i.e. covering a large state space), while the goal-conditioned policy learns to minimize the temporal distance to the goal (i.e. reaching the goal). Our experimental results in six simulated robotic locomotion environments demonstrate that our method significantly outperforms previous unsupervised GCRL methods in achieving a wide variety of states.

This paper presents three open-source reinforcement learning environments developed on the MuJoCo physics engine with the Franka Emika Panda arm in MuJoCo Menagerie. Three representative tasks, push, slide, and pick-and-place, are implemented through the Gymnasium Robotics API, which inherits from the core of Gymnasium. Both the sparse binary and dense rewards are supported, and the observation space contains the keys of desired and achieved goals to follow the Multi-Goal Reinforcement Learning framework. Three different off-policy algorithms are used to validate the simulation attributes to ensure the fidelity of all tasks, and benchmark results are also given. Each environment and task are defined in a clean way, and the main parameters for modifying the environment are preserved to reflect the main difference. The repository, including all environments, is available at https://github.com/zichunxx/panda_mujoco_gym.

We study what actually works and what doesn't for training large language models as agents via multi-turn reinforcement learning. Despite rapid progress, existing frameworks and definitions are fragmented, and there is no systematic formulation or analysis of which design choices matter across tasks. We address this gap by first breaking down the design space into three inter-related pillars -- environment, reward, and policy -- and empirically derive a recipe for training LLM agents in situated textual domains. In particular, we test TextWorld and ALFWorld, popular domains for testing situated embodied reasoning, as well as SWE-Gym for more software engineering style tasks. (i) For the environment, we analyze the impacts of task complexity in terms of sizes of the state and action spaces as well as optimal solution length, finding that even simple environments within a domain can provide signal on how well an agent can generalize to more complex tasks. (ii) For the reward, we ablate relative reward sparsity, observing that while dense turn-level rewards accelerate training, performance and stability is highly dependent on the choice of RL algorithm. (iii) And for the agent's policy, we explore the interplay between reward sparsity and biased (PPO, GRPO) and unbiased (RLOO) policy gradient methods in addition to showing how to find the optimal Supervised Fine-tuning (SFT) to RL training ratio given a fixed budget. We distill these findings into a training recipe that guides co-design across the three pillars, facilitating research and practical efforts in multi-turn agentic RL. Code: https://github.com/pearls-lab/meow-tea-taro

Reward sparsity in long-horizon reinforcement learning (RL) tasks remains a significant challenge, while existing outcome-based reward shaping struggles to define meaningful immediate rewards without introducing bias or requiring explicit task decomposition. Alternatively, verification-based reward shaping uses stepwise critics, but misalignment between immediate rewards and long-term objectives can lead to reward hacking and suboptimal policies. In this work, we address this problem in the context of software engineering (SWE) tasks, where multi-turn reasoning and rule-based verification are critical. We introduce the SWE-oriented RL Framework, a unified system supporting multi-turn interaction, docker-based execution, and customizable reward functions. Additionally, we propose Gated Reward Accumulation (G-RA), a novel method that accumulates immediate rewards only when high-level (long-term) rewards meet a predefined threshold, ensuring stable RL optimization. Experiments on SWE-bench Verified and kBench demonstrate that G-RA leads to an increase in completion rates (47.6\% \rightarrow 93.8\% and 22.0\% \rightarrow 86.0\%) and modification rates (19.6\% \rightarrow 23.8\% and 12.0\% \rightarrow 42.0\%), while avoiding policy degradation caused by reward misalignment. Our findings highlight the importance of balanced reward accumulation in long-horizon RL and provide a practical solution.

We consider the problem of decentralized multi-agent reinforcement learning in Markov games. A fundamental question is whether there exist algorithms that, when adopted by all agents and run independently in a decentralized fashion, lead to no-regret for each player, analogous to celebrated convergence results in normal-form games. While recent work has shown that such algorithms exist for restricted settings (notably, when regret is defined with respect to deviations to Markovian policies), the question of whether independent no-regret learning can be achieved in the standard Markov game framework was open. We provide a decisive negative resolution this problem, both from a computational and statistical perspective. We show that: - Under the widely-believed assumption that PPAD-hard problems cannot be solved in polynomial time, there is no polynomial-time algorithm that attains no-regret in general-sum Markov games when executed independently by all players, even when the game is known to the algorithm designer and the number of players is a small constant. - When the game is unknown, no algorithm, regardless of computational efficiency, can achieve no-regret without observing a number of episodes that is exponential in the number of players. Perhaps surprisingly, our lower bounds hold even for seemingly easier setting in which all agents are controlled by a a centralized algorithm. They are proven via lower bounds for a simpler problem we refer to as SparseCCE, in which the goal is to compute a coarse correlated equilibrium that is sparse in the sense that it can be represented as a mixture of a small number of product policies. The crux of our approach is a novel application of aggregation techniques from online learning, whereby we show that any algorithm for the SparseCCE problem can be used to compute approximate Nash equilibria for non-zero sum normal-form games.

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in R^d that approximate the rewards in a bandit or RL with a uniform error of varepsilon, searching for an O(varepsilon)-optimal action requires pulling at least Omega(exp(d)) queries. Furthermore, Lattimore et al. (2020) show that a degraded O(varepsilond)-optimal solution can be learned within poly(d/varepsilon) queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the varepsilond barrier. In this paper, we address this question by showing that algorithms can obtain O(varepsilon)-optimal actions by querying O(varepsilon^{-s}d^s) actions, where s is the sparsity parameter, removing the exp(d)-dependence. We then establish information-theoretical lower bounds, i.e., Omega(exp(s)), to show that our upper bound on sample complexity is nearly tight if one demands an error O(s^{delta}varepsilon) for 0<delta<1. For deltageq 1, we further show that poly(s/varepsilon) queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

Current reinforcement learning from human feedback (RLHF) pipelines for large language model (LLM) alignment typically assign scalar rewards to sequences, using the final token as a surrogate indicator for the quality of the entire sequence. However, this leads to sparse feedback and suboptimal token-level credit assignment. In this work, we frame reward shaping as an optimization problem focused on token-level credit assignment. We propose a reward-shaping function leveraging explainability methods such as SHAP and LIME to estimate per-token rewards from the reward model. To learn parameters of this shaping function, we employ a bilevel optimization framework that integrates Bayesian Optimization and policy training to handle noise from the token reward estimates. Our experiments show that achieving a better balance of token-level reward attribution leads to performance improvements over baselines on downstream tasks and finds an optimal policy faster during training. Furthermore, we show theoretically that explainability methods that are feature additive attribution functions maintain the optimal policy as the original reward.

Reinforcement learning (RL) has been widely used in text generation to alleviate the exposure bias issue or to utilize non-parallel datasets. The reward function plays an important role in making RL training successful. However, previous reward functions are typically task-specific and sparse, restricting the use of RL. In our work, we propose a task-agnostic approach that derives a step-wise reward function directly from a model trained with teacher forcing. We additionally propose a simple modification to stabilize the RL training on non-parallel datasets with our induced reward function. Empirical results show that our method outperforms self-training and reward regression methods on several text generation tasks, confirming the effectiveness of our reward function.

We present a fine-grained theoretical analysis of the performance gap between reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) under a representation gap. Our study decomposes this gap into two sources: an explicit representation gap under exact optimization and an implicit representation gap under finite samples. In the exact optimization setting, we characterize how the relative capacities of the reward and policy model classes influence the final policy qualities. We show that RLHF, DPO, or online DPO can outperform one another depending on the type of model mis-specifications. Notably, online DPO can outperform both RLHF and standard DPO when the reward and policy model classes are isomorphic and both mis-specified. In the approximate optimization setting, we provide a concrete construction where the ground-truth reward is implicitly sparse and show that RLHF requires significantly fewer samples than DPO to recover an effective reward model -- highlighting a statistical advantage of two-stage learning. Together, these results provide a comprehensive understanding of the performance gap between RLHF and DPO under various settings, and offer practical insights into when each method is preferred.

Recent works have successfully demonstrated that sparse deep reinforcement learning agents can be competitive against their dense counterparts. This opens up opportunities for reinforcement learning applications in fields where inference time and memory requirements are cost-sensitive or limited by hardware. Until now, dense-to-sparse methods have relied on hand-designed sparsity schedules that are not synchronized with the agent's learning pace. Crucially, the final sparsity level is chosen as a hyperparameter, which requires careful tuning as setting it too high might lead to poor performances. In this work, we address these shortcomings by crafting a dense-to-sparse algorithm that we name Eau De Q-Network (EauDeQN). To increase sparsity at the agent's learning pace, we consider multiple online networks with different sparsity levels, where each online network is trained from a shared target network. At each target update, the online network with the smallest loss is chosen as the next target network, while the other networks are replaced by a pruned version of the chosen network. We evaluate the proposed approach on the Atari 2600 benchmark and the MuJoCo physics simulator, showing that EauDeQN reaches high sparsity levels while keeping performances high.

Dynamical generative models that produce samples through an iterative process, such as Flow Matching and denoising diffusion models, have seen widespread use, but there have not been many theoretically-sound methods for improving these models with reward fine-tuning. In this work, we cast reward fine-tuning as stochastic optimal control (SOC). Critically, we prove that a very specific memoryless noise schedule must be enforced during fine-tuning, in order to account for the dependency between the noise variable and the generated samples. We also propose a new algorithm named Adjoint Matching which outperforms existing SOC algorithms, by casting SOC problems as a regression problem. We find that our approach significantly improves over existing methods for reward fine-tuning, achieving better consistency, realism, and generalization to unseen human preference reward models, while retaining sample diversity.

We present a general convergent class of reinforcement learning algorithms that is founded on two distinct principles: (1) mapping value estimates to a different space using arbitrary functions from a broad class, and (2) linearly decomposing the reward signal into multiple channels. The first principle enables incorporating specific properties into the value estimator that can enhance learning. The second principle, on the other hand, allows for the value function to be represented as a composition of multiple utility functions. This can be leveraged for various purposes, e.g. dealing with highly varying reward scales, incorporating a priori knowledge about the sources of reward, and ensemble learning. Combining the two principles yields a general blueprint for instantiating convergent algorithms by orchestrating diverse mapping functions over multiple reward channels. This blueprint generalizes and subsumes algorithms such as Q-Learning, Log Q-Learning, and Q-Decomposition. In addition, our convergence proof for this general class relaxes certain required assumptions in some of these algorithms. Based on our theory, we discuss several interesting configurations as special cases. Finally, to illustrate the potential of the design space that our theory opens up, we instantiate a particular algorithm and evaluate its performance on the Atari suite.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn behavior alignment reward functions. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality -- some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

One of the challenges in applying reinforcement learning in a complex real-world environment lies in providing the agent with a sufficiently detailed reward function. Any misalignment between the reward and the desired behavior can result in unwanted outcomes. This may lead to issues like "reward hacking" where the agent maximizes rewards by unintended behavior. In this work, we propose to disentangle the reward into two distinct parts. A simple task-specific reward, outlining the particulars of the task at hand, and an unknown common-sense reward, indicating the expected behavior of the agent within the environment. We then explore how this common-sense reward can be learned from expert demonstrations. We first show that inverse reinforcement learning, even when it succeeds in training an agent, does not learn a useful reward function. That is, training a new agent with the learned reward does not impair the desired behaviors. We then demonstrate that this problem can be solved by training simultaneously on multiple tasks. That is, multi-task inverse reinforcement learning can be applied to learn a useful reward function.

Reinforcement learning (RL) often encounters delayed and sparse feedback in real-world applications, even with only episodic rewards. Previous approaches have made some progress in reward redistribution for credit assignment but still face challenges, including training difficulties due to redundancy and ambiguous attributions stemming from overlooking the multifaceted nature of mission performance evaluation. Hopefully, Large Language Model (LLM) encompasses fruitful decision-making knowledge and provides a plausible tool for reward redistribution. Even so, deploying LLM in this case is non-trivial due to the misalignment between linguistic knowledge and the symbolic form requirement, together with inherent randomness and hallucinations in inference. To tackle these issues, we introduce LaRe, a novel LLM-empowered symbolic-based decision-making framework, to improve credit assignment. Key to LaRe is the concept of the Latent Reward, which works as a multi-dimensional performance evaluation, enabling more interpretable goal attainment from various perspectives and facilitating more effective reward redistribution. We examine that semantically generated code from LLM can bridge linguistic knowledge and symbolic latent rewards, as it is executable for symbolic objects. Meanwhile, we design latent reward self-verification to increase the stability and reliability of LLM inference. Theoretically, reward-irrelevant redundancy elimination in the latent reward benefits RL performance from more accurate reward estimation. Extensive experimental results witness that LaRe (i) achieves superior temporal credit assignment to SOTA methods, (ii) excels in allocating contributions among multiple agents, and (iii) outperforms policies trained with ground truth rewards for certain tasks.

Large language model (LLM)-based agents are increasingly trained with reinforcement learning (RL) to enhance their ability to interact with external environments through tool use, particularly in search-based settings that require multi-turn reasoning and knowledge acquisition. However, existing approaches typically rely on outcome-based rewards that are only provided at the final answer. This reward sparsity becomes particularly problematic in multi-turn settings, where long trajectories exacerbate two critical issues: (i) advantage collapse, where all rollouts receive identical rewards and provide no useful learning signals, and (ii) lack of fine-grained credit assignment, where dependencies between turns are obscured, especially in long-horizon tasks. In this paper, we propose Information Gain-based Policy Optimization (IGPO), a simple yet effective RL framework that provides dense and intrinsic supervision for multi-turn agent training. IGPO models each interaction turn as an incremental process of acquiring information about the ground truth, and defines turn-level rewards as the marginal increase in the policy's probability of producing the correct answer. Unlike prior process-level reward approaches that depend on external reward models or costly Monte Carlo estimation, IGPO derives intrinsic rewards directly from the model's own belief updates. These intrinsic turn-level rewards are combined with outcome-level supervision to form dense reward trajectories. Extensive experiments on both in-domain and out-of-domain benchmarks demonstrate that IGPO consistently outperforms strong baselines in multi-turn scenarios, achieving higher accuracy and improved sample efficiency.

Reward models trained on human preference data have been proven to be effective for aligning Large Language Models (LLMs) with human intent within the reinforcement learning from human feedback (RLHF) framework. However, the generalization capabilities of current reward models to unseen prompts and responses are limited. This limitation can lead to an unexpected phenomenon known as reward over-optimization, where excessive optimization of rewards results in a decline in actual performance. While previous research has advocated for constraining policy optimization, our study proposes a novel approach to enhance the reward model's generalization ability against distribution shifts by regularizing the hidden states. Specifically, we retain the base model's language model head and incorporate a suite of text-generation losses to preserve the hidden states' text generation capabilities, while concurrently learning a reward head behind the same hidden states. Our experimental results demonstrate that the introduced regularization technique markedly improves the accuracy of learned reward models across a variety of out-of-distribution (OOD) tasks and effectively alleviate the over-optimization issue in RLHF, offering a more reliable and robust preference learning paradigm.

Reinforcement fine-tuning (RFT) often suffers from reward over-optimization, where a policy model hacks the reward signals to achieve high scores while producing low-quality outputs. Our theoretical analysis shows that the key lies in reward misspecification at the high-reward tail: the inability to reliably distinguish Excellent responses from merely Great ones. This motivate us to focus on the high-reward region. However, such tail examples are scarce under the base LLM. While off-policy exemplars (e.g. from stronger models or rewrites) are easier to obtain, naively training on them yields a misspecified reward for the policy we aim to align. To address this, we study rubric-based rewards. By design, rubrics can leverage off-policy examples while remaining insensitive to their artifacts. To elicit rubrics that capture the high-reward tail, we highlight the importance of distinguishing among great and diverse responses, and introduce a workflow to implement this idea. We empirically demonstrate that rubric-based rewards substantially mitigate reward over-optimization and deliver effective LLM post-training improvements. Our code can be accessed at https://github.com/Jun-Kai-Zhang/rubrics.git .

Specifying rewards for reinforcement learned (RL) agents is challenging. Preference-based RL (PbRL) mitigates these challenges by inferring a reward from feedback over sets of trajectories. However, the effectiveness of PbRL is limited by the amount of feedback needed to reliably recover the structure of the target reward. We present the PRIor Over Rewards (PRIOR) framework, which incorporates priors about the structure of the reward function and the preference feedback into the reward learning process. Imposing these priors as soft constraints on the reward learning objective reduces the amount of feedback required by half and improves overall reward recovery. Additionally, we demonstrate that using an abstract state space for the computation of the priors further improves the reward learning and the agent's performance.

Graphical User Interface (GUI) grounding maps natural language instructions to precise interface locations for autonomous interaction. Current reinforcement learning approaches use binary rewards that treat elements as hit-or-miss targets, creating sparse signals that ignore the continuous nature of spatial interactions. Motivated by human clicking behavior that naturally forms Gaussian distributions centered on target elements, we introduce GUI Gaussian Grounding Rewards (GUI-G^2), a principled reward framework that models GUI elements as continuous Gaussian distributions across the interface plane. GUI-G^2 incorporates two synergistic mechanisms: Gaussian point rewards model precise localization through exponentially decaying distributions centered on element centroids, while coverage rewards assess spatial alignment by measuring the overlap between predicted Gaussian distributions and target regions. To handle diverse element scales, we develop an adaptive variance mechanism that calibrates reward distributions based on element dimensions. This framework transforms GUI grounding from sparse binary classification to dense continuous optimization, where Gaussian distributions generate rich gradient signals that guide models toward optimal interaction positions. Extensive experiments across ScreenSpot, ScreenSpot-v2, and ScreenSpot-Pro benchmarks demonstrate that GUI-G^2, substantially outperforms state-of-the-art method UI-TARS-72B, with the most significant improvement of 24.7% on ScreenSpot-Pro. Our analysis reveals that continuous modeling provides superior robustness to interface variations and enhanced generalization to unseen layouts, establishing a new paradigm for spatial reasoning in GUI interaction tasks.

Large Language Models (LLMs) increasingly rely on external tools such as search engines to solve complex agentic tasks that require reasoning and external knowledge retrieval. Recently, reinforcement learning with verifiable rewards (RLVR) has demonstrated its effectiveness in advancing capabilities of LLMs by rewarding the final answers via outcome rewards. While straightforward to supervise, outcome rewards only provide sparse signals and delayed feedback, which limits their effectiveness on long trajectories. Process rewards address this by evaluating intermediate steps, providing fine-grained supervision and encouraging grounded problem solving. However, it is notoriously hard to annotate step-wise labels, especially in non-verifiable process without "golden" answers. Furthermore, step-wise judgment requires the balance between local quality with contribution to the final outcome, as optimizing towards higher process reward may not always align with better final outcomes. To address the above challenges, we introduce Principle Process Reward (PPR), an RL approach that unifies principled step-level assessment and outcome verification. We train a principle-based reward model to improve the transparency and reliability of process evaluation, and further introduce a Reward Normalization (ReNorm) strategy to calibrate outcome and process rewards. Experiment results show that PPR achieves state-of-the-art performance across a wide range of benchmarks, demonstrating its impressive robustness and generalization. Our code and model collection is available in this link.

Large language models (LLMs) are increasingly trained with reinforcement learning (RL) as autonomous agents that reason and act over long horizons in interactive environments. However, sparse and sometimes unverifiable rewards make temporal credit assignment extremely challenging. Recent work attempts to integrate process supervision into agent learning but suffers from biased annotation, reward hacking, high-variance from overly fine-grained signals or failtures when state overlap is rare. We therefore introduce Online Process Reward Learning (OPRL), a general credit-assignment strategy for agentic RL that integrates seamlessly with standard on-policy algorithms without relying on additional rollouts or explicit step labels. In OPRL, we optimize an implicit process reward model (PRM) alternately with the agent's policy to transform trajectory preferences into implicit step rewards through a trajectory-based DPO objective. These step rewards are then used to compute step-level advantages, which are combined with episode-level advantages from outcome rewards for policy update, creating a self-reinforcing loop. Theoretical findings guarantee that the learned step rewards are consistent with trajectory preferences and act as potential-based shaping rewards, providing bounded gradients to stabilize training. Empirically, we evaluate OPRL on three distinct agent benmarks, including WebShop and VisualSokoban, as well as open-ended social interactions with unverfiable rewards in SOTOPIA. Crucially, OPRL shows superior performance over frontier LLMs and strong RL baselines across domains, achieving state-of-the-art results with higher sample-efficiency and lower variance during training. Further analysis also demonstrates the efficient exploration by OPRL using fewer actions, underscoring its potential for agentic learning in real-world scenarios.

In the last decade, Deep Reinforcement Learning has evolved into a powerful tool for complex sequential decision-making problems. It combines deep learning's proficiency in processing rich input signals with reinforcement learning's adaptability across diverse control tasks. At its core, an RL agent seeks to maximize its cumulative reward, enabling AI algorithms to uncover novel solutions previously unknown to experts. However, this focus on reward maximization also introduces a significant difficulty: improper reward specification can result in unexpected, misaligned agent behavior and inefficient learning. The complexity of accurately specifying the reward function is further amplified by the sequential nature of the task, the sparsity of learning signals, and the multifaceted aspects of the desired behavior. In this thesis, we survey the literature on effective reward specification strategies, identify core challenges relating to each of these approaches, and propose original contributions addressing the issue of sample efficiency and alignment in deep reinforcement learning. Reward specification represents one of the most challenging aspects of applying reinforcement learning in real-world domains. Our work underscores the absence of a universal solution to this complex and nuanced challenge; solving it requires selecting the most appropriate tools for the specific requirements of each unique application.

Vision-Language Models (VLMs) often suffer from visual hallucinations, saying things that are not actually in the image, and language shortcuts, where they skip the visual part and just rely on text priors. These issues arise because most post-training methods for VLMs rely on simple verifiable answer matching and supervise only final outputs, leaving intermediate visual reasoning without explicit guidance. As a result, VLMs receive sparse visual signals and often learn to prioritize language-based reasoning over visual perception. To mitigate this, some existing methods add visual supervision using human annotations or distilled labels from external large models. However, human annotations are labor-intensive and costly, and because external signals cannot adapt to the evolving policy, they cause distributional shifts that can lead to reward hacking. In this paper, we introduce Vision-SR1, a self-rewarding method that improves visual reasoning without relying on external visual supervisions via reinforcement learning. Vision-SR1 decomposes VLM reasoning into two stages: visual perception and language reasoning. The model is first prompted to produce self-contained visual perceptions that are sufficient to answer the question without referring back the input image. To validate this self-containment, the same VLM model is then re-prompted to perform language reasoning using only the generated perception as input to compute reward. This self-reward is combined with supervision on final outputs, providing a balanced training signal that strengthens both visual perception and language reasoning. Our experiments demonstrate that Vision-SR1 improves visual reasoning, mitigates visual hallucinations, and reduces reliance on language shortcuts across diverse vision-language tasks.

Learning from human preference has been considered key to aligning Large Language Models (LLMs) with human values. However, contrary to popular belief, our preliminary study reveals that reward models trained on human preference datasets tend to give higher scores to long off-topic responses than short on-topic ones. Motivated by this observation, we explore a preference-free approach utilizing `relevance' as a key objective for alignment. On our first attempt, we find that the relevance score obtained by a retriever alone is vulnerable to reward hacking, i.e., overoptimizing to undesired shortcuts, when we utilize the score as a reward for reinforcement learning. To mitigate it, we integrate effective inductive biases into the vanilla relevance to regularize each other, resulting in a mixture of reward functions: Regularized Relevance Reward (R^3). R^3 significantly improves performance on preference benchmarks by providing a robust reward signal. Notably, R^3 does not require any human preference datasets (i.e., preference-free), outperforming open-source reward models in improving human preference. Our analysis demonstrates that R^3 has advantages in elevating human preference while minimizing its side effects. Finally, we show the generalizability of R^3, consistently improving instruction-tuned models in various backbones and sizes without additional dataset cost. Our code is available at https://github.com/naver-ai/RRR.

The performance of the reward model (RM) is a critical factor in improving the effectiveness of the large language model (LLM) during alignment fine-tuning. There remain two challenges in RM training: 1) training the same RM using various categories of data may cause its generalization performance to suffer from multi-task disturbance, and 2) the human annotation consistency rate is generally only 60% to 75%, causing training data to contain a lot of noise. To tackle these two challenges, we introduced the idea of Mixture-of-Experts (MoE) into the field of RM for the first time. We propose the Double-Layer MoE RM (DMoERM). The outer layer MoE is a sparse model. After classifying an input into task categories, we route it to the corresponding inner layer task-specific model. The inner layer MoE is a dense model. We decompose the specific task into multiple capability dimensions and individually fine-tune a LoRA expert on each one. Their outputs are then synthesized by an MLP to compute the final rewards. To minimize costs, we call a public LLM API to obtain the capability preference labels. The validation on manually labeled datasets confirms that our model attains superior consistency with human preference and outstrips advanced generative approaches. Meanwhile, through BoN sampling and RL experiments, we demonstrate that our model outperforms state-of-the-art ensemble methods of RM and mitigates the overoptimization problem. Our code and dataset are available at: https://github.com/quanshr/DMoERM-v1.

Pretrained language models are commonly aligned with human preferences and downstream tasks via reinforcement finetuning (RFT), which entails maximizing a (possibly learned) reward function using policy gradient algorithms. This work highlights a fundamental optimization obstacle in RFT: we prove that the expected gradient for an input vanishes when its reward standard deviation under the model is small, even if the expected reward is far from optimal. Through experiments on an RFT benchmark and controlled environments, as well as a theoretical analysis, we then demonstrate that vanishing gradients due to small reward standard deviation are prevalent and detrimental, leading to extremely slow reward maximization. Lastly, we explore ways to overcome vanishing gradients in RFT. We find the common practice of an initial supervised finetuning (SFT) phase to be the most promising candidate, which sheds light on its importance in an RFT pipeline. Moreover, we show that a relatively small number of SFT optimization steps on as few as 1% of the input samples can suffice, indicating that the initial SFT phase need not be expensive in terms of compute and data labeling efforts. Overall, our results emphasize that being mindful for inputs whose expected gradient vanishes, as measured by the reward standard deviation, is crucial for successful execution of RFT.

In this work, we study the issue of reward hacking on the response length, a challenge emerging in Reinforcement Learning from Human Feedback (RLHF) on LLMs. A well-formatted, verbose but less helpful response from the LLMs can often deceive LLMs or even human evaluators to achieve high scores. The same issue also holds for some reward models in RL. To address the challenges in both training and evaluation, we establish a more reliable evaluation protocol for comparing different training configurations, which inspects the trade-off between LLM evaluation score and response length obtained by varying training hyperparameters. Based on this evaluation, we conduct large-scale studies, where the results shed insights into the efficacy of hyperparameters and tricks used in RL on mitigating length bias. We further propose to improve the reward model by jointly training two linear heads on shared feature representations to predict the rewards, one trained to correlate with length, and the other trained to decorrelate with length and therefore focus more on the actual content. We then discard the length head in RL to prevent reward hacking on length. Experiments demonstrate that our approach almost eliminates the reward correlation with length, and improves the obtained policy by a significant margin.

Reinforcement learning (RL) holds significant promise for training LLM agents to handle complex, goal-oriented tasks that require multi-step interactions with external environments. However, a critical challenge when applying RL to these agentic tasks arises from delayed rewards: feedback signals are typically available only after the entire task is completed. This makes it non-trivial to assign delayed rewards to earlier actions, providing insufficient guidance regarding environmental constraints and hindering agent training. In this work, we draw on the insight that the ultimate completion of a task emerges from the cumulative progress an agent makes across individual steps. We propose Stepwise Progress Attribution (SPA), a general reward redistribution framework that decomposes the final reward into stepwise contributions, each reflecting its incremental progress toward overall task completion. To achieve this, we train a progress estimator that accumulates stepwise contributions over a trajectory to match the task completion. During policy optimization, we combine the estimated per-step contribution with a grounding signal for actions executed in the environment as the fine-grained, intermediate reward for effective agent training. Extensive experiments on common agent benchmarks (including Webshop, ALFWorld, and VirtualHome) demonstrate that SPA consistently outperforms the state-of-the-art method in both success rate (+2.5\% on average) and grounding accuracy (+1.9\% on average). Further analyses demonstrate that our method remarkably provides more effective intermediate rewards for RL training. Our code is available at https://github.com/WangHanLinHenry/SPA-RL-Agent.

Although RLVR has become an essential component for developing advanced reasoning skills in LLMs, contemporary studies have documented training plateaus that emerge following thousands of optimization steps, demonstrating notable decreases in performance gains despite increased computational investment. This limitation stems from the sparse exploration patterns inherent in current RLVR practices, where models rely on limited rollouts that often miss critical reasoning paths and fail to provide systematic coverage of the solution space. We present DeepSearch, a framework that integrates Monte Carlo Tree Search directly into RLVR training. In contrast to existing methods that rely on tree search only at inference, DeepSearch embeds structured search into the training loop, enabling systematic exploration and fine-grained credit assignment across reasoning steps. Through training-time exploration, DeepSearch addresses the fundamental bottleneck of insufficient exploration, which leads to diminishing performance improvements over prolonged training steps. Our contributions include: (1) a global frontier selection strategy that prioritizes promising nodes across the search tree, (2) selection with entropy-based guidance that identifies confident paths for supervision, and (3) adaptive replay buffer training with solution caching for efficiency. Experiments on mathematical reasoning benchmarks show that DeepSearch achieves 62.95% average accuracy and establishes a new state-of-the-art for 1.5B reasoning models - using 5.7x fewer GPU hours than extended training approaches. These results highlight the importance of strategic exploration over brute-force scaling and demonstrate the promise of algorithmic innovation for advancing RLVR methodologies. DeepSearch establishes a new direction for scaling reasoning capabilities through systematic search rather than prolonged computation.

Preference alignment in Large Language Models (LLMs) has significantly improved their ability to adhere to human instructions and intentions. However, existing direct alignment algorithms primarily focus on relative preferences and often overlook the qualitative aspects of responses. Striving to maximize the implicit reward gap between the chosen and the slightly inferior rejected responses can cause overfitting and unnecessary unlearning of the high-quality rejected responses. The unawareness of the reward scores also drives the LLM to indiscriminately favor the low-quality chosen responses and fail to generalize to responses with the highest rewards, which are sparse in data. To overcome these shortcomings, our study introduces reward-conditioned LLM policies that discern and learn from the entire spectrum of response quality within the dataset, helping extrapolate to more optimal regions. We propose an effective yet simple data relabeling method that conditions the preference pairs on quality scores to construct a reward-augmented dataset. This dataset is easily integrated with existing direct alignment algorithms and is applicable to any preference dataset. The experimental results across instruction-following benchmarks including AlpacaEval, MT-Bench, and Arena-Hard-Auto demonstrate that our approach consistently boosts the performance of DPO by a considerable margin across diverse models. Additionally, our method improves the average accuracy on various academic benchmarks. When applying our method to on-policy data, the resulting DPO model achieves SOTA results on AlpacaEval. Through ablation studies, we demonstrate that our method not only maximizes the utility of preference data but also mitigates the issue of unlearning, demonstrating its broad effectiveness beyond mere dataset expansion. Our code is available at https://github.com/shenao-zhang/reward-augmented-preference.

This paper studies post-training large language models (LLMs) using preference feedback from a powerful oracle to help a model iteratively improve over itself. The typical approach for post-training LLMs involves Reinforcement Learning from Human Feedback (RLHF), which traditionally separates reward learning and subsequent policy optimization. However, such a reward maximization approach is limited by the nature of "point-wise" rewards (such as Bradley-Terry model), which fails to express complex intransitive or cyclic preference relations. While advances on RLHF show reward learning and policy optimization can be merged into a single contrastive objective for stability, they yet still remain tethered to the reward maximization framework. Recently, a new wave of research sidesteps the reward maximization presumptions in favor of directly optimizing over "pair-wise" or general preferences. In this paper, we introduce Direct Nash Optimization (DNO), a provable and scalable algorithm that marries the simplicity and stability of contrastive learning with theoretical generality from optimizing general preferences. Because DNO is a batched on-policy algorithm using a regression-based objective, its implementation is straightforward and efficient. Moreover, DNO enjoys monotonic improvement across iterations that help it improve even over a strong teacher (such as GPT-4). In our experiments, a resulting 7B parameter Orca-2.5 model aligned by DNO achieves the state-of-the-art win-rate against GPT-4-Turbo of 33% on AlpacaEval 2.0 (even after controlling for response length), an absolute gain of 26% (7% to 33%) over the initializing model. It outperforms models with far more parameters, including Mistral Large, Self-Rewarding LM (70B parameters), and older versions of GPT-4.

Inverse reinforcement learning (IRL) denotes a powerful family of algorithms for recovering a reward function justifying the behavior demonstrated by an expert agent. A well-known limitation of IRL is the ambiguity in the choice of the reward function, due to the existence of multiple rewards that explain the observed behavior. This limitation has been recently circumvented by formulating IRL as the problem of estimating the feasible reward set, i.e., the region of the rewards compatible with the expert's behavior. In this paper, we make a step towards closing the theory gap of IRL in the case of finite-horizon problems with a generative model. We start by formally introducing the problem of estimating the feasible reward set, the corresponding PAC requirement, and discussing the properties of particular classes of rewards. Then, we provide the first minimax lower bound on the sample complexity for the problem of estimating the feasible reward set of order {Omega}Bigl( H^3SA{epsilon^2} bigl( log bigl(1{delta}bigl) + S bigl)Bigl), being S and A the number of states and actions respectively, H the horizon, epsilon the desired accuracy, and delta the confidence. We analyze the sample complexity of a uniform sampling strategy (US-IRL), proving a matching upper bound up to logarithmic factors. Finally, we outline several open questions in IRL and propose future research directions.

Reinforcement learning (RL) has become a standard paradigm for refining large language models (LLMs) beyond pre-training and instruction tuning. A prominent line of work is RL with verifiable rewards (RLVR), which leverages automatically verifiable outcomes (e.g., correctness or executability) to generate reward signals. While efficient, this framework faces two key limitations: First, its binary feedback is too sparse to capture the quality of the reasoning process. Second, its coarse-grained rewards potentially lead to vanishing gradients. Inspired by observations from human learning, we introduce a RL technique that integrates verifiable outcomes with the model's own confidence estimates. This joint design enriches the reward signal, providing finer-grained feedback and implicitly supervising the reasoning process. Experimental results demonstrate that our proposed method enhances RL performance across multiple datasets and reduces token consumption during inference, while incurring negligible additional training cost. Moreover, it can be used as a plug-in module to enhance other state-of-the-art RL methods.

Search agents powered by Large Language Models (LLMs) have demonstrated significant potential in tackling knowledge-intensive tasks. Reinforcement learning (RL) has emerged as a powerful paradigm for training these agents to perform complex, multi-step reasoning. However, prior RL-based methods often rely on sparse or rule-based rewards, which can lead agents to commit to suboptimal or erroneous reasoning paths without the ability to recover. To address these limitations, we propose ReSeek, a novel self-correcting framework for training search agents. Our framework introduces a self-correction mechanism that empowers the agent to dynamically identify and recover from erroneous search paths during an episode. By invoking a special JUDGE action, the agent can judge the information and re-plan its search strategy. To guide this process, we design a dense, instructive process reward function, which decomposes into a correctness reward for retrieving factual information and a utility reward for finding information genuinely useful for the query. Furthermore, to mitigate the risk of data contamination in existing datasets, we introduce FictionalHot, a new and challenging benchmark with recently curated questions requiring complex reasoning. Being intuitively reasonable and practically simple, extensive experiments show that agents trained with ReSeek significantly outperform SOTA baselines in task success rate and path faithfulness.

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates with probabilities proportional to a given reward. However, GFlowNets can only be used with a predefined scalar reward, which can be either computationally expensive or not directly accessible, in the case of multi-objective optimization (MOO) tasks for example. Moreover, to prioritize identifying high-reward candidates, the conventional practice is to raise the reward to a higher exponent, the optimal choice of which may vary across different environments. To address these issues, we propose Order-Preserving GFlowNets (OP-GFNs), which sample with probabilities in proportion to a learned reward function that is consistent with a provided (partial) order on the candidates, thus eliminating the need for an explicit formulation of the reward function. We theoretically prove that the training process of OP-GFNs gradually sparsifies the learned reward landscape in single-objective maximization tasks. The sparsification concentrates on candidates of a higher hierarchy in the ordering, ensuring exploration at the beginning and exploitation towards the end of the training. We demonstrate OP-GFN's state-of-the-art performance in single-objective maximization (totally ordered) and multi-objective Pareto front approximation (partially ordered) tasks, including synthetic datasets, molecule generation, and neural architecture search.

Avatars are important to create interactive and immersive experiences in virtual worlds. One challenge in animating these characters to mimic a user's motion is that commercial AR/VR products consist only of a headset and controllers, providing very limited sensor data of the user's pose. Another challenge is that an avatar might have a different skeleton structure than a human and the mapping between them is unclear. In this work we address both of these challenges. We introduce a method to retarget motions in real-time from sparse human sensor data to characters of various morphologies. Our method uses reinforcement learning to train a policy to control characters in a physics simulator. We only require human motion capture data for training, without relying on artist-generated animations for each avatar. This allows us to use large motion capture datasets to train general policies that can track unseen users from real and sparse data in real-time. We demonstrate the feasibility of our approach on three characters with different skeleton structure: a dinosaur, a mouse-like creature and a human. We show that the avatar poses often match the user surprisingly well, despite having no sensor information of the lower body available. We discuss and ablate the important components in our framework, specifically the kinematic retargeting step, the imitation, contact and action reward as well as our asymmetric actor-critic observations. We further explore the robustness of our method in a variety of settings including unbalancing, dancing and sports motions.

Preference Optimization (PO) has proven an effective step for aligning language models to human-desired behaviors. Current variants, following the offline Direct Preference Optimization objective, have focused on a strict setting where all tokens are contributing signals of KL divergence and rewards to the loss function. However, human preference is not affected by each word in a sequence equally but is often dependent on specific words or phrases, e.g. existence of toxic terms leads to non-preferred responses. Based on this observation, we argue that not all tokens should be weighted equally during PO and propose a flexible objective termed SparsePO, that aims to automatically learn to weight the KL divergence and reward corresponding to each token during PO training. We propose two different variants of weight-masks that can either be derived from the reference model itself or learned on the fly. Notably, our method induces sparsity in the learned masks, allowing the model to learn how to best weight reward and KL divergence contributions at the token level, learning an optimal level of mask sparsity. Extensive experiments on multiple domains, including sentiment control, dialogue, text summarization and text-to-code generation, illustrate that our approach assigns meaningful weights to tokens according to the target task, generates more responses with the desired preference and improves reasoning tasks by up to 2 percentage points compared to other token- and response-level PO methods.

Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of Bayesian optimisation by leveraging data from related tasks. While previous methods successfully meta-learn either a surrogate model or an acquisition function independently, joint training of both components remains an open challenge. This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data. Early on, we notice that training transformer-based neural processes from scratch with RL is challenging due to insufficient supervision, especially when rewards are sparse. We formalise this claim with a combinatorial analysis showing that the widely used notion of regret as a reward signal exhibits a logarithmic sparsity pattern in trajectory lengths. To tackle this problem, we augment the RL objective with an auxiliary task that guides part of the architecture to learn a valid probabilistic model as an inductive bias. We demonstrate that our method achieves state-of-the-art regret results against various baselines in experiments on standard hyperparameter optimisation tasks and also outperforms others in the real-world problems of mixed-integer programming tuning, antibody design, and logic synthesis for electronic design automation.

Despite the recent success of reinforcement learning in various domains, these approaches remain, for the most part, deterringly sensitive to hyper-parameters and are often riddled with essential engineering feats allowing their success. We consider the case of off-policy generative adversarial imitation learning, and perform an in-depth review, qualitative and quantitative, of the method. We show that forcing the learned reward function to be local Lipschitz-continuous is a sine qua non condition for the method to perform well. We then study the effects of this necessary condition and provide several theoretical results involving the local Lipschitzness of the state-value function. We complement these guarantees with empirical evidence attesting to the strong positive effect that the consistent satisfaction of the Lipschitzness constraint on the reward has on imitation performance. Finally, we tackle a generic pessimistic reward preconditioning add-on spawning a large class of reward shaping methods, which makes the base method it is plugged into provably more robust, as shown in several additional theoretical guarantees. We then discuss these through a fine-grained lens and share our insights. Crucially, the guarantees derived and reported in this work are valid for any reward satisfying the Lipschitzness condition, nothing is specific to imitation. As such, these may be of independent interest.

Reinforcement Learning from Verifiable Rewards (RLVR) has been widely adopted as the de facto method for enhancing the reasoning capabilities of large language models and has demonstrated notable success in verifiable domains like math and competitive programming tasks. However, the efficacy of RLVR diminishes significantly when applied to agentic environments. These settings, characterized by multi-step, complex problem solving, lead to high failure rates even for frontier LLMs, as the reward landscape is too sparse for effective model training via conventional RLVR. In this work, we introduce Agent-RLVR, a framework that makes RLVR effective in challenging agentic settings, with an initial focus on software engineering tasks. Inspired by human pedagogy, Agent-RLVR introduces agent guidance, a mechanism that actively steers the agent towards successful trajectories by leveraging diverse informational cues. These cues, ranging from high-level strategic plans to dynamic feedback on the agent's errors and environmental interactions, emulate a teacher's guidance, enabling the agent to navigate difficult solution spaces and promotes active self-improvement via additional environment exploration. In the Agent-RLVR training loop, agents first attempt to solve tasks to produce initial trajectories, which are then validated by unit tests and supplemented with agent guidance. Agents then reattempt with guidance, and the agent policy is updated with RLVR based on the rewards of these guided trajectories. Agent-RLVR elevates the pass@1 performance of Qwen-2.5-72B-Instruct from 9.4% to 22.4% on SWE-Bench Verified. We find that our guidance-augmented RLVR data is additionally useful for test-time reward model training, shown by further boosting pass@1 to 27.8%. Agent-RLVR lays the groundwork for training agents with RLVR in complex, real-world environments where conventional RL methods struggle.

Implementing a reward function that perfectly captures a complex task in the real world is impractical. As a result, it is often appropriate to think of the reward function as a proxy for the true objective rather than as its definition. We study this phenomenon through the lens of Goodhart's law, which predicts that increasing optimisation of an imperfect proxy beyond some critical point decreases performance on the true objective. First, we propose a way to quantify the magnitude of this effect and show empirically that optimising an imperfect proxy reward often leads to the behaviour predicted by Goodhart's law for a wide range of environments and reward functions. We then provide a geometric explanation for why Goodhart's law occurs in Markov decision processes. We use these theoretical insights to propose an optimal early stopping method that provably avoids the aforementioned pitfall and derive theoretical regret bounds for this method. Moreover, we derive a training method that maximises worst-case reward, for the setting where there is uncertainty about the true reward function. Finally, we evaluate our early stopping method experimentally. Our results support a foundation for a theoretically-principled study of reinforcement learning under reward misspecification.

Large language models are typically aligned with human preferences by optimizing reward models (RMs) fitted to human feedback. However, human preferences are multi-faceted, and it is increasingly common to derive reward from a composition of simpler reward models which each capture a different aspect of language quality. This itself presents a challenge, as it is difficult to appropriately weight these component RMs when combining them. Compounding this difficulty, because any RM is only a proxy for human evaluation, this process is vulnerable to overoptimization, wherein past a certain point, accumulating higher reward is associated with worse human ratings. In this paper, we perform, to our knowledge, the first study on overoptimization in composite RMs, showing that correlation between component RMs has a significant effect on the locations of these points. We then introduce an approach to solve this issue using constrained reinforcement learning as a means of preventing the agent from exceeding each RM's threshold of usefulness. Our method addresses the problem of weighting component RMs by learning dynamic weights, naturally expressed by Lagrange multipliers. As a result, each RM stays within the range at which it is an effective proxy, improving evaluation performance. Finally, we introduce an adaptive method using gradient-free optimization to identify and optimize towards these points during a single run.

Ensuring sufficient exploration is a central challenge when training meta-reinforcement learning (meta-RL) agents to solve novel environments. Conventional solutions to the exploration-exploitation dilemma inject explicit incentives such as randomization, uncertainty bonuses, or intrinsic rewards to encourage exploration. In this work, we hypothesize that an agent trained solely to maximize a greedy (exploitation-only) objective can nonetheless exhibit emergent exploratory behavior, provided three conditions are met: (1) Recurring Environmental Structure, where the environment features repeatable regularities that allow past experience to inform future choices; (2) Agent Memory, enabling the agent to retain and utilize historical interaction data; and (3) Long-Horizon Credit Assignment, where learning propagates returns over a time frame sufficient for the delayed benefits of exploration to inform current decisions. Through experiments in stochastic multi-armed bandits and temporally extended gridworlds, we observe that, when both structure and memory are present, a policy trained on a strictly greedy objective exhibits information-seeking exploratory behavior. We further demonstrate, through controlled ablations, that emergent exploration vanishes if either environmental structure or agent memory is absent (Conditions 1 & 2). Surprisingly, removing long-horizon credit assignment (Condition 3) does not always prevent emergent exploration-a result we attribute to the pseudo-Thompson Sampling effect. These findings suggest that, under the right prerequisites, exploration and exploitation need not be treated as orthogonal objectives but can emerge from a unified reward-maximization process.

Reward design in reinforcement learning (RL) is challenging since specifying human notions of desired behavior may be difficult via reward functions or require many expert demonstrations. Can we instead cheaply design rewards using a natural language interface? This paper explores how to simplify reward design by prompting a large language model (LLM) such as GPT-3 as a proxy reward function, where the user provides a textual prompt containing a few examples (few-shot) or a description (zero-shot) of the desired behavior. Our approach leverages this proxy reward function in an RL framework. Specifically, users specify a prompt once at the beginning of training. During training, the LLM evaluates an RL agent's behavior against the desired behavior described by the prompt and outputs a corresponding reward signal. The RL agent then uses this reward to update its behavior. We evaluate whether our approach can train agents aligned with user objectives in the Ultimatum Game, matrix games, and the DealOrNoDeal negotiation task. In all three tasks, we show that RL agents trained with our framework are well-aligned with the user's objectives and outperform RL agents trained with reward functions learned via supervised learning

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

We investigate reinforcement learning (RL) for privileged planning in autonomous driving. State-of-the-art approaches for this task are rule-based, but these methods do not scale to the long tail. RL, on the other hand, is scalable and does not suffer from compounding errors like imitation learning. Contemporary RL approaches for driving use complex shaped rewards that sum multiple individual rewards, \eg~progress, position, or orientation rewards. We show that PPO fails to optimize a popular version of these rewards when the mini-batch size is increased, which limits the scalability of these approaches. Instead, we propose a new reward design based primarily on optimizing a single intuitive reward term: route completion. Infractions are penalized by terminating the episode or multiplicatively reducing route completion. We find that PPO scales well with higher mini-batch sizes when trained with our simple reward, even improving performance. Training with large mini-batch sizes enables efficient scaling via distributed data parallelism. We scale PPO to 300M samples in CARLA and 500M samples in nuPlan with a single 8-GPU node. The resulting model achieves 64 DS on the CARLA longest6 v2 benchmark, outperforming other RL methods with more complex rewards by a large margin. Requiring only minimal adaptations from its use in CARLA, the same method is the best learning-based approach on nuPlan. It scores 91.3 in non-reactive and 90.6 in reactive traffic on the Val14 benchmark while being an order of magnitude faster than prior work.

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in inefficient optimization process. In this work, we investigate the function of process reward models (PRMs) to accelerate the RL training for LRMs. We propose a novel intrinsic signal-driven generative process evaluation mechanism operating at the thought level to address major bottlenecks in RL-based training. Specifically, instead of requiring PRMs to know how to solve problems, our method uses intrinsic signals in solutions to judge stepwise correctness and aggregate contiguous correct/incorrect steps into coherent 'thought' units. This structured, thought-level rewards enable more reliable credit assignment by reducing ambiguity in step segmentation and alleviating reward hacking. We further introduce a capability-adaptive reward mechanism that dynamically balances exploration and exploitation based on the LRM's current proficiency, guiding learning without stifling creative trial-and-error. These innovations are integrated into a new off-policy RL algorithm, TP-GRPO, which extends grouped proximal optimization with process-based rewards and improves training efficiency. Experiments on 1.5B and 7B parameter LRMs demonstrate that our method achieves higher problem-solving accuracy with significantly fewer training samples than outcome-only reward baselines. The results validate that well-structured process rewards can substantially accelerate LRM optimization in math reasoning tasks. Code is available at https://github.com/cs-holder/tp_grpo.

Reinforcement Learning from Human Feedback (RLHF) is essential for aligning large language models (LLMs) with human values. However, RLHF is susceptible to reward hacking, where the agent exploits flaws in the reward function rather than learning the intended behavior, thus degrading alignment. While reward shaping helps stabilize RLHF and partially mitigate reward hacking, a systematic investigation into shaping techniques and their underlying principles remains lacking. To bridge this gap, we present a comprehensive study of the prevalent reward shaping methods. Our analysis suggests three key design principles: (1) RL reward is ideally bounded, (2) RL benefits from rapid initial growth followed by gradual convergence, and (3) RL reward is best formulated as a function of centered reward. Guided by these insights, we propose Preference As Reward (PAR), a novel approach that leverages the latent preferences embedded within the reward model itself as the signal for reinforcement learning. We evaluated PAR on two base models, Gemma2-2B and Llama3-8B, using two datasets, Ultrafeedback-Binarized and HH-RLHF. Experimental results demonstrate PAR's superior performance over other reward shaping methods. On the AlpacaEval 2.0 benchmark, PAR achieves a win rate at least 5 percentage points higher than competing approaches. Furthermore, PAR exhibits remarkable data efficiency, requiring only a single reference reward for optimal performance, and maintains robustness against reward hacking even after two full epochs of training. Code is available at https://github.com/PorUna-byte/PAR.

We present Direct Reward Fine-Tuning (DRaFT), a simple and effective method for fine-tuning diffusion models to maximize differentiable reward functions, such as scores from human preference models. We first show that it is possible to backpropagate the reward function gradient through the full sampling procedure, and that doing so achieves strong performance on a variety of rewards, outperforming reinforcement learning-based approaches. We then propose more efficient variants of DRaFT: DRaFT-K, which truncates backpropagation to only the last K steps of sampling, and DRaFT-LV, which obtains lower-variance gradient estimates for the case when K=1. We show that our methods work well for a variety of reward functions and can be used to substantially improve the aesthetic quality of images generated by Stable Diffusion 1.4. Finally, we draw connections between our approach and prior work, providing a unifying perspective on the design space of gradient-based fine-tuning algorithms.

Multi-armed bandits a simple but very powerful framework for algorithms that make decisions over time under uncertainty. An enormous body of work has accumulated over the years, covered in several books and surveys. This book provides a more introductory, textbook-like treatment of the subject. Each chapter tackles a particular line of work, providing a self-contained, teachable technical introduction and a brief review of the further developments; many of the chapters conclude with exercises. The book is structured as follows. The first four chapters are on IID rewards, from the basic model to impossibility results to Bayesian priors to Lipschitz rewards. The next three chapters cover adversarial rewards, from the full-feedback version to adversarial bandits to extensions with linear rewards and combinatorially structured actions. Chapter 8 is on contextual bandits, a middle ground between IID and adversarial bandits in which the change in reward distributions is completely explained by observable contexts. The last three chapters cover connections to economics, from learning in repeated games to bandits with supply/budget constraints to exploration in the presence of incentives. The appendix provides sufficient background on concentration and KL-divergence. The chapters on "bandits with similarity information", "bandits with knapsacks" and "bandits and agents" can also be consumed as standalone surveys on the respective topics.

Recent advances in aligning Large Language Models with human preferences have benefited from larger reward models and better preference data. However, most of these methodologies rely on the accuracy of the reward model. The reward models used in Reinforcement Learning with Human Feedback (RLHF) are typically learned from small datasets using stochastic optimization algorithms, making them prone to high variability. We illustrate the inconsistencies between reward models empirically on numerous open-source datasets. We theoretically show that the fluctuation of the reward models can be detrimental to the alignment problem because the derived policies are more overfitted to the reward model and, hence, are riskier if the reward model itself is uncertain. We use concentration of measure to motivate an uncertainty-aware, conservative algorithm for policy optimization. We show that such policies are more risk-averse in the sense that they are more cautious of uncertain rewards. We theoretically prove that our proposed methodology has less risk than the vanilla method. We corroborate our theoretical results with experiments based on designing an ensemble of reward models. We use this ensemble of reward models to align a language model using our methodology and observe that our empirical findings match our theoretical predictions.

In reinforcement learning (RL), rewards of states are typically considered additive, and following the Markov assumption, they are independent of states visited previously. In many important applications, such as coverage control, experiment design and informative path planning, rewards naturally have diminishing returns, i.e., their value decreases in light of similar states visited previously. To tackle this, we propose submodular RL (SubRL), a paradigm which seeks to optimize more general, non-additive (and history-dependent) rewards modelled via submodular set functions which capture diminishing returns. Unfortunately, in general, even in tabular settings, we show that the resulting optimization problem is hard to approximate. On the other hand, motivated by the success of greedy algorithms in classical submodular optimization, we propose SubPO, a simple policy gradient-based algorithm for SubRL that handles non-additive rewards by greedily maximizing marginal gains. Indeed, under some assumptions on the underlying Markov Decision Process (MDP), SubPO recovers optimal constant factor approximations of submodular bandits. Moreover, we derive a natural policy gradient approach for locally optimizing SubRL instances even in large state- and action- spaces. We showcase the versatility of our approach by applying SubPO to several applications, such as biodiversity monitoring, Bayesian experiment design, informative path planning, and coverage maximization. Our results demonstrate sample efficiency, as well as scalability to high-dimensional state-action spaces.

DeepSeek-R1 has successfully enhanced Large Language Model (LLM) reasoning capabilities through its rule-based reward system. While it's a ''perfect'' reward system that effectively mitigates reward hacking, such reward functions are often discrete. Our experimental observations suggest that discrete rewards can lead to gradient anomaly, unstable optimization, and slow convergence. To address this issue, we propose ReDit (Reward Dithering), a method that dithers the discrete reward signal by adding simple random noise. With this perturbed reward, exploratory gradients are continuously provided throughout the learning process, enabling smoother gradient updates and accelerating convergence. The injected noise also introduces stochasticity into flat reward regions, encouraging the model to explore novel policies and escape local optima. Experiments across diverse tasks demonstrate the effectiveness and efficiency of ReDit. On average, ReDit achieves performance comparable to vanilla GRPO with only approximately 10% the training steps, and furthermore, still exhibits a 4% performance improvement over vanilla GRPO when trained for a similar duration. Visualizations confirm significant mitigation of gradient issues with ReDit. Moreover, theoretical analyses are provided to further validate these advantages.

Two main challenges in Reinforcement Learning (RL) are designing appropriate reward functions and ensuring the safety of the learned policy. To address these challenges, we present a theoretical framework for Inverse Reinforcement Learning (IRL) in constrained Markov decision processes. From a convex-analytic perspective, we extend prior results on reward identifiability and generalizability to both the constrained setting and a more general class of regularizations. In particular, we show that identifiability up to potential shaping (Cao et al., 2021) is a consequence of entropy regularization and may generally no longer hold for other regularizations or in the presence of safety constraints. We also show that to ensure generalizability to new transition laws and constraints, the true reward must be identified up to a constant. Additionally, we derive a finite sample guarantee for the suboptimality of the learned rewards, and validate our results in a gridworld environment.

Significant progress in reward modeling over recent years has been driven by a paradigm shift from task-specific designs towards generalist reward models. Despite this trend, developing effective reward models remains a fundamental challenge: the heavy reliance on large-scale labeled preference data. Pre-training on abundant unlabeled data offers a promising direction, but existing approaches fall short of instilling explicit reasoning into reward models. To bridge this gap, we propose a self-training approach that leverages unlabeled data to elicit reward reasoning in reward models. Based on this approach, we develop GRAM-R^2, a generative reward model trained to produce not only preference labels but also accompanying reward rationales. GRAM-R^2 can serve as a foundation model for reward reasoning and can be applied to a wide range of tasks with minimal or no additional fine-tuning. It can support downstream applications such as response ranking and task-specific reward tuning. Experiments on response ranking, task adaptation, and reinforcement learning from human feedback demonstrate that GRAM-R^2 consistently delivers strong performance, outperforming several strong discriminative and generative baselines.

In this paper, we focus on the task of conditional image generation, where an image is synthesized according to user instructions. The critical challenge underpinning this task is ensuring both the fidelity of the generated images and their semantic alignment with the provided conditions. To tackle this issue, previous studies have employed supervised perceptual losses derived from pre-trained models, i.e., reward models, to enforce alignment between the condition and the generated result. However, we observe one inherent shortcoming: considering the diversity of synthesized images, the reward model usually provides inaccurate feedback when encountering newly generated data, which can undermine the training process. To address this limitation, we propose an uncertainty-aware reward modeling, called Ctrl-U, including uncertainty estimation and uncertainty-aware regularization, designed to reduce the adverse effects of imprecise feedback from the reward model. Given the inherent cognitive uncertainty within reward models, even images generated under identical conditions often result in a relatively large discrepancy in reward loss. Inspired by the observation, we explicitly leverage such prediction variance as an uncertainty indicator. Based on the uncertainty estimation, we regularize the model training by adaptively rectifying the reward. In particular, rewards with lower uncertainty receive higher loss weights, while those with higher uncertainty are given reduced weights to allow for larger variability. The proposed uncertainty regularization facilitates reward fine-tuning through consistency construction. Extensive experiments validate the effectiveness of our methodology in improving the controllability and generation quality, as well as its scalability across diverse conditional scenarios. Code will soon be available at https://grenoble-zhang.github.io/Ctrl-U-Page/.

In this work, we consider the problem of collaborative multi-user reinforcement learning. In this setting there are multiple users with the same state-action space and transition probabilities but with different rewards. Under the assumption that the reward matrix of the N users has a low-rank structure -- a standard and practically successful assumption in the offline collaborative filtering setting -- the question is can we design algorithms with significantly lower sample complexity compared to the ones that learn the MDP individually for each user. Our main contribution is an algorithm which explores rewards collaboratively with N user-specific MDPs and can learn rewards efficiently in two key settings: tabular MDPs and linear MDPs. When N is large and the rank is constant, the sample complexity per MDP depends logarithmically over the size of the state-space, which represents an exponential reduction (in the state-space size) when compared to the standard ``non-collaborative'' algorithms.

Using reinforcement learning with human feedback (RLHF) has shown significant promise in fine-tuning diffusion models. Previous methods start by training a reward model that aligns with human preferences, then leverage RL techniques to fine-tune the underlying models. However, crafting an efficient reward model demands extensive datasets, optimal architecture, and manual hyperparameter tuning, making the process both time and cost-intensive. The direct preference optimization (DPO) method, effective in fine-tuning large language models, eliminates the necessity for a reward model. However, the extensive GPU memory requirement of the diffusion model's denoising process hinders the direct application of the DPO method. To address this issue, we introduce the Direct Preference for Denoising Diffusion Policy Optimization (D3PO) method to directly fine-tune diffusion models. The theoretical analysis demonstrates that although D3PO omits training a reward model, it effectively functions as the optimal reward model trained using human feedback data to guide the learning process. This approach requires no training of a reward model, proving to be more direct, cost-effective, and minimizing computational overhead. In experiments, our method uses the relative scale of objectives as a proxy for human preference, delivering comparable results to methods using ground-truth rewards. Moreover, D3PO demonstrates the ability to reduce image distortion rates and generate safer images, overcoming challenges lacking robust reward models.

Text-to-SQL is a challenging task involving multiple reasoning-intensive subtasks, including natural language understanding, database schema comprehension, and precise SQL query formulation. Existing approaches often rely on handcrafted reasoning paths with inductive biases that can limit their overall effectiveness. Motivated by the recent success of reasoning-enhanced models such as DeepSeek R1 and OpenAI o1, which effectively leverage reward-driven self-exploration to enhance reasoning capabilities and generalization, we propose a novel set of partial rewards tailored specifically for the Text-to-SQL task. Our reward set includes schema-linking, AI feedback, n-gram similarity, and syntax check, explicitly designed to address the reward sparsity issue prevalent in reinforcement learning (RL). Leveraging group relative policy optimization (GRPO), our approach explicitly encourages large language models (LLMs) to develop intrinsic reasoning skills necessary for accurate SQL query generation. With models of different sizes, we demonstrate that RL-only training with our proposed rewards consistently achieves higher accuracy and superior generalization compared to supervised fine-tuning (SFT). Remarkably, our RL-trained 14B-parameter model significantly outperforms larger proprietary models, e.g. o3-mini by 4% and Gemini-1.5-Pro-002 by 3% on the BIRD benchmark. These highlight the efficacy of our proposed RL-training framework with partial rewards for enhancing both accuracy and reasoning capabilities in Text-to-SQL tasks.

Current Large Language Models (LLMs) often undergo supervised fine-tuning (SFT) to acquire tool use capabilities. However, SFT struggles to generalize to unfamiliar or complex tool use scenarios. Recent advancements in reinforcement learning (RL), particularly with R1-like models, have demonstrated promising reasoning and generalization abilities. Yet, reward design for tool use presents unique challenges: multiple tools may be invoked with diverse parameters, and coarse-grained reward signals, such as answer matching, fail to offer the finegrained feedback required for effective learning. In this work, we present the first comprehensive study on reward design for tool selection and application tasks within the RL paradigm. We systematically explore a wide range of reward strategies, analyzing their types, scales, granularity, and temporal dynamics. Building on these insights, we propose a principled reward design tailored for tool use tasks and apply it to train LLMs using Group Relative Policy Optimization (GRPO). Empirical evaluations across diverse benchmarks demonstrate that our approach yields robust, scalable, and stable training, achieving a 17% improvement over base models and a 15% gain over SFT models. These results highlight the critical role of thoughtful reward design in enhancing the tool use capabilities and generalization performance of LLMs. All the codes are released to facilitate future research.

Recent studies have demonstrated the effectiveness of directly aligning diffusion models with human preferences using differentiable reward. However, they exhibit two primary challenges: (1) they rely on multistep denoising with gradient computation for reward scoring, which is computationally expensive, thus restricting optimization to only a few diffusion steps; (2) they often need continuous offline adaptation of reward models in order to achieve desired aesthetic quality, such as photorealism or precise lighting effects. To address the limitation of multistep denoising, we propose Direct-Align, a method that predefines a noise prior to effectively recover original images from any time steps via interpolation, leveraging the equation that diffusion states are interpolations between noise and target images, which effectively avoids over-optimization in late timesteps. Furthermore, we introduce Semantic Relative Preference Optimization (SRPO), in which rewards are formulated as text-conditioned signals. This approach enables online adjustment of rewards in response to positive and negative prompt augmentation, thereby reducing the reliance on offline reward fine-tuning. By fine-tuning the FLUX.1.dev model with optimized denoising and online reward adjustment, we improve its human-evaluated realism and aesthetic quality by over 3x.

We study a strategic variant of the multi-armed bandit problem, which we coin the strategic click-bandit. This model is motivated by applications in online recommendation where the choice of recommended items depends on both the click-through rates and the post-click rewards. Like in classical bandits, rewards follow a fixed unknown distribution. However, we assume that the click-rate of each arm is chosen strategically by the arm (e.g., a host on Airbnb) in order to maximize the number of times it gets clicked. The algorithm designer does not know the post-click rewards nor the arms' actions (i.e., strategically chosen click-rates) in advance, and must learn both values over time. To solve this problem, we design an incentive-aware learning algorithm, UCB-S, which achieves two goals simultaneously: (a) incentivizing desirable arm behavior under uncertainty; (b) minimizing regret by learning unknown parameters. We characterize all approximate Nash equilibria among arms under UCB-S and show a mathcal{O} (KT) regret bound uniformly in every equilibrium. We also show that incentive-unaware algorithms generally fail to achieve low regret in the strategic click-bandit. Finally, we support our theoretical results by simulations of strategic arm behavior which confirm the effectiveness and robustness of our proposed incentive design.

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by 1, we show that our algorithm only needs to explore tilde O( d^2varepsilon^{-2}) episodes to find an varepsilon-optimal policy, where d is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is ``horizon-free''. In addition, we provide an Omega(d^2varepsilon^{-2}) sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

We study a distributed stochastic multi-armed bandit where a client supplies the learner with communication-constrained feedback based on the rewards for the corresponding arm pulls. In our setup, the client must encode the rewards such that the second moment of the encoded rewards is no more than P, and this encoded reward is further corrupted by additive Gaussian noise of variance sigma^2; the learner only has access to this corrupted reward. For this setting, we derive an information-theoretic lower bound of Omegaleft(frac{KT{SNR wedge1}} right) on the minimax regret of any scheme, where SNR := P{sigma^2}, and K and T are the number of arms and time horizon, respectively. Furthermore, we propose a multi-phase bandit algorithm, UEtext{-UCB++}, which matches this lower bound to a minor additive factor. UEtext{-UCB++} performs uniform exploration in its initial phases and then utilizes the {\em upper confidence bound }(UCB) bandit algorithm in its final phase. An interesting feature of UEtext{-UCB++} is that the coarser estimates of the mean rewards formed during a uniform exploration phase help to refine the encoding protocol in the next phase, leading to more accurate mean estimates of the rewards in the subsequent phase. This positive reinforcement cycle is critical to reducing the number of uniform exploration rounds and closely matching our lower bound.

In order to solve a task using reinforcement learning, it is necessary to first formalise the goal of that task as a reward function. However, for many real-world tasks, it is very difficult to manually specify a reward function that never incentivises undesirable behaviour. As a result, it is increasingly popular to use reward learning algorithms, which attempt to learn a reward function from data. However, the theoretical foundations of reward learning are not yet well-developed. In particular, it is typically not known when a given reward learning algorithm with high probability will learn a reward function that is safe to optimise. This means that reward learning algorithms generally must be evaluated empirically, which is expensive, and that their failure modes are difficult to anticipate in advance. One of the roadblocks to deriving better theoretical guarantees is the lack of good methods for quantifying the difference between reward functions. In this paper we provide a solution to this problem, in the form of a class of pseudometrics on the space of all reward functions that we call STARC (STAndardised Reward Comparison) metrics. We show that STARC metrics induce both an upper and a lower bound on worst-case regret, which implies that our metrics are tight, and that any metric with the same properties must be bilipschitz equivalent to ours. Moreover, we also identify a number of issues with reward metrics proposed by earlier works. Finally, we evaluate our metrics empirically, to demonstrate their practical efficacy. STARC metrics can be used to make both theoretical and empirical analysis of reward learning algorithms both easier and more principled.

Recent developments in Large Language Models (LLMs) have shifted from pre-training scaling to post-training and test-time scaling. Across these developments, a key unified paradigm has arisen: Learning from Rewards, where reward signals act as the guiding stars to steer LLM behavior. It has underpinned a wide range of prevalent techniques, such as reinforcement learning (in RLHF, DPO, and GRPO), reward-guided decoding, and post-hoc correction. Crucially, this paradigm enables the transition from passive learning from static data to active learning from dynamic feedback. This endows LLMs with aligned preferences and deep reasoning capabilities. In this survey, we present a comprehensive overview of the paradigm of learning from rewards. We categorize and analyze the strategies under this paradigm across training, inference, and post-inference stages. We further discuss the benchmarks for reward models and the primary applications. Finally we highlight the challenges and future directions. We maintain a paper collection at https://github.com/bobxwu/learning-from-rewards-llm-papers.

Optimizing the presentation of search and recommendation results is crucial to enhancing user experience and engagement. Whole Page Optimization (WPO) plays a pivotal role in this process, as it directly influences how information is surfaced to users. While Pre-trained Large Language Models (LLMs) have demonstrated remarkable capabilities in generating coherent and contextually relevant content, fine-tuning these models for complex tasks like WPO presents challenges. Specifically, the need for extensive human-annotated data to mitigate issues such as hallucinations and model instability can be prohibitively expensive, especially in large-scale systems that interact with millions of items daily. In this work, we address the challenge of fine-tuning LLMs for WPO by using user feedback as the supervision. Unlike manually labeled datasets, user feedback is inherently noisy and less precise. To overcome this, we propose a reward-based fine-tuning approach, PageLLM, which employs a mixed-grained reward mechanism that combines page-level and item-level rewards. The page-level reward evaluates the overall quality and coherence, while the item-level reward focuses on the accuracy and relevance of key recommendations. This dual-reward structure ensures that both the holistic presentation and the critical individual components are optimized. We validate PageLLM on both public and industrial datasets. PageLLM outperforms baselines and achieves a 0.44\% GMV increase in an online A/B test with over 10 million users, demonstrating its real-world impact.

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose (1+epsilon)-th moment is bounded for some epsilonin (0,1]. Although there exist methods for generalized linear bandits, most of them focus on bounded or sub-Gaussian rewards and are not well-suited for many real-world scenarios, such as financial markets and web-advertising. To address this issue, we propose two novel algorithms based on truncation and mean of medians. These algorithms achieve an almost optimal regret bound of O(dT^{1{1+epsilon}}), where d is the dimension of contextual information and T is the time horizon. Our truncation-based algorithm supports online learning, distinguishing it from existing truncation-based approaches. Additionally, our mean-of-medians-based algorithm requires only O(log T) rewards and one estimator per epoch, making it more practical. Moreover, our algorithms improve the regret bounds by a logarithmic factor compared to existing algorithms when epsilon=1. Numerical experimental results confirm the merits of our algorithms.

In machine learning, the notion of multi-armed bandits refers to a class of online learning problems, in which an agent is supposed to simultaneously explore and exploit a given set of choice alternatives in the course of a sequential decision process. In the standard setting, the agent learns from stochastic feedback in the form of real-valued rewards. In many applications, however, numerical reward signals are not readily available -- instead, only weaker information is provided, in particular relative preferences in the form of qualitative comparisons between pairs of alternatives. This observation has motivated the study of variants of the multi-armed bandit problem, in which more general representations are used both for the type of feedback to learn from and the target of prediction. The aim of this paper is to provide a survey of the state of the art in this field, referred to as preference-based multi-armed bandits or dueling bandits. To this end, we provide an overview of problems that have been considered in the literature as well as methods for tackling them. Our taxonomy is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback.

Large language models (LLMs) increasingly rely on thinking models that externalize intermediate steps and allocate extra test-time compute, with think-twice strategies showing that a deliberate second pass can elicit stronger reasoning. In contrast, most reward models (RMs) still compress many quality dimensions into a single scalar in one shot, a design that induces judgment diffusion: attention spreads across evaluation criteria, yielding diluted focus and shallow analysis. We introduce branch-and-rethink (BR-RM), a two-turn RM that transfers the think-twice principle to reward modeling. Turn 1 performs adaptive branching, selecting a small set of instance-critical dimensions (such as factuality and safety) and sketching concise, evidence-seeking hypotheses. Turn 2 executes branch-conditioned rethinking, a targeted reread that tests those hypotheses and scrutinizes only what matters most. We train with GRPO-style reinforcement learning over structured two-turn traces using a simple binary outcome reward with strict format checks, making the approach compatible with standard RLHF pipelines. By converting all-at-oncescoringintofocused, second-lookreasoning, BR-RMreducesjudgmentdiffusionandimproves sensitivity to subtle yet consequential errors while remaining practical and scalable. Experimental results demonstrate that our model achieves state-of-the-art performance on three challenging reward modeling benchmarks across diverse domains. The code and the model will be released soon.

Diffusion models produce impressive results in modalities ranging from images and video to protein design and text. However, generating samples with user-specified properties remains a challenge. Recent research proposes fine-tuning models to maximize rewards that capture desired properties, but these methods require expensive training and are prone to mode collapse. In this work, we propose Feynman Kac (FK) steering, an inference-time framework for steering diffusion models with reward functions. FK steering works by sampling a system of multiple interacting diffusion processes, called particles, and resampling particles at intermediate steps based on scores computed using functions called potentials. Potentials are defined using rewards for intermediate states and are selected such that a high value indicates that the particle will yield a high-reward sample. We explore various choices of potentials, intermediate rewards, and samplers. We evaluate FK steering on text-to-image and text diffusion models. For steering text-to-image models with a human preference reward, we find that FK steering a 0.8B parameter model outperforms a 2.6B parameter fine-tuned model on prompt fidelity, with faster sampling and no training. For steering text diffusion models with rewards for text quality and specific text attributes, we find that FK steering generates lower perplexity, more linguistically acceptable outputs and enables gradient-free control of attributes like toxicity. Our results demonstrate that inference-time scaling and steering of diffusion models, even with off-the-shelf rewards, can provide significant sample quality gains and controllability benefits. Code is available at https://github.com/zacharyhorvitz/Fk-Diffusion-Steering .

While Large Language Models (LLMs) hold promise to become autonomous agents, they often explore suboptimally in sequential decision-making. Recent work has sought to enhance this capability via supervised fine-tuning (SFT) or reinforcement learning (RL), improving regret on the classic multi-armed bandit task. However, it remains unclear how these learning methods shape exploration strategies and how well they generalize. We investigate both paradigms by training LLMs with SFT on expert trajectories and RL with a range of tailored reward signals including a strategic, regret-shaped reward to reduce variance, and an algorithmic reward that enables oracle imitation. The resulting agents outperform pre-trained models and achieve performance comparable to Upper Confidence Bound (UCB) and Thompson Sampling, with robust generalization to 6x longer horizons and across bandit families. Behavioral analysis reveals that gains often stem from more sophisticated but greedier exploitation: RL/SFT agents are more prone to early catastrophic failure than pre-trained models, prematurely abandoning exploration. Furthermore, agents trained to imitate UCB learn to outperform their teacher by adopting more exploitative variants. Our findings clarify when each training paradigm is preferable and advocate tailored reward design and evaluation beyond average regret to promote robust exploratory behavior.

Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an epsilon-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make significant progress on minimizing simple regret in both data-rich (Tge n) and data-poor regime (T le n) where n is the number of arms, and T is the number of samples. At its heart is our improved instance-dependent analysis of the well-known Sequential Halving (SH) algorithm, where we bound the probability of returning an arm whose mean reward is not within epsilon from the best (i.e., not epsilon-good) for any choice of epsilon>0, although epsilon is not an input to SH. Our bound not only leads to an optimal worst-case simple regret bound of n/T up to logarithmic factors but also essentially matches the instance-dependent lower bound for returning an epsilon-good arm reported by Katz-Samuels and Jamieson (2020). For the more challenging data-poor regime, we propose Bracketing SH (BSH) that enjoys the same improvement even without sampling each arm at least once. Our empirical study shows that BSH outperforms existing methods on real-world tasks.

Reinforcement learning (RL) requires either manually specifying a reward function, which is often infeasible, or learning a reward model from a large amount of human feedback, which is often very expensive. We study a more sample-efficient alternative: using pretrained vision-language models (VLMs) as zero-shot reward models (RMs) to specify tasks via natural language. We propose a natural and general approach to using VLMs as reward models, which we call VLM-RMs. We use VLM-RMs based on CLIP to train a MuJoCo humanoid to learn complex tasks without a manually specified reward function, such as kneeling, doing the splits, and sitting in a lotus position. For each of these tasks, we only provide a single sentence text prompt describing the desired task with minimal prompt engineering. We provide videos of the trained agents at: https://sites.google.com/view/vlm-rm. We can improve performance by providing a second ``baseline'' prompt and projecting out parts of the CLIP embedding space irrelevant to distinguish between goal and baseline. Further, we find a strong scaling effect for VLM-RMs: larger VLMs trained with more compute and data are better reward models. The failure modes of VLM-RMs we encountered are all related to known capability limitations of current VLMs, such as limited spatial reasoning ability or visually unrealistic environments that are far off-distribution for the VLM. We find that VLM-RMs are remarkably robust as long as the VLM is large enough. This suggests that future VLMs will become more and more useful reward models for a wide range of RL applications.

We posit that to achieve superhuman agents, future models require superhuman feedback in order to provide an adequate training signal. Current approaches commonly train reward models from human preferences, which may then be bottlenecked by human performance level, and secondly these separate frozen reward models cannot then learn to improve during LLM training. In this work, we study Self-Rewarding Language Models, where the language model itself is used via LLM-as-a-Judge prompting to provide its own rewards during training. We show that during Iterative DPO training that not only does instruction following ability improve, but also the ability to provide high-quality rewards to itself. Fine-tuning Llama 2 70B on three iterations of our approach yields a model that outperforms many existing systems on the AlpacaEval 2.0 leaderboard, including Claude 2, Gemini Pro, and GPT-4 0613. While only a preliminary study, this work opens the door to the possibility of models that can continually improve in both axes.

Traditionally, reward models used for reinforcement learning from human feedback (RLHF) are trained to directly predict preference scores without leveraging the generation capabilities of the underlying large language model (LLM). This limits the capabilities of reward models as they must reason implicitly about the quality of a response, i.e., preference modeling must be performed in a single forward pass through the model. To enable reward models to reason explicitly about the quality of a response, we introduce Critique-out-Loud (CLoud) reward models. CLoud reward models operate by first generating a natural language critique of the assistant's response that is then used to predict a scalar reward for the quality of the response. We demonstrate the success of CLoud reward models for both Llama-3-8B and 70B base models: compared to classic reward models CLoud reward models improve pairwise preference classification accuracy on RewardBench by 4.65 and 5.84 percentage points for the 8B and 70B base models respectively. Furthermore, CLoud reward models lead to a Pareto improvement for win rate on ArenaHard when used as the scoring model for Best-of-N. Finally, we explore how to exploit the dynamic inference compute capabilities of CLoud reward models by performing self-consistency decoding for reward prediction.

We propose Flow-GRPO, the first method integrating online reinforcement learning (RL) into flow matching models. Our approach uses two key strategies: (1) an ODE-to-SDE conversion that transforms a deterministic Ordinary Differential Equation (ODE) into an equivalent Stochastic Differential Equation (SDE) that matches the original model's marginal distribution at all timesteps, enabling statistical sampling for RL exploration; and (2) a Denoising Reduction strategy that reduces training denoising steps while retaining the original inference timestep number, significantly improving sampling efficiency without performance degradation. Empirically, Flow-GRPO is effective across multiple text-to-image tasks. For complex compositions, RL-tuned SD3.5 generates nearly perfect object counts, spatial relations, and fine-grained attributes, boosting GenEval accuracy from 63% to 95%. In visual text rendering, its accuracy improves from 59% to 92%, significantly enhancing text generation. Flow-GRPO also achieves substantial gains in human preference alignment. Notably, little to no reward hacking occurred, meaning rewards did not increase at the cost of image quality or diversity, and both remained stable in our experiments.

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an untrained policy impedes discriminator learning. We call this learning setting Internally Rewarded Reinforcement Learning (IRRL) as the reward is not provided directly by the environment but internally by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

Despite notable advancements in Multimodal Large Language Models (MLLMs), most state-of-the-art models have not undergone thorough alignment with human preferences. This gap exists because current alignment research has primarily achieved progress in specific areas (e.g., hallucination reduction), while the broader question of whether aligning models with human preferences can systematically enhance MLLM capability remains largely unexplored. To this end, we introduce MM-RLHF, a dataset containing 120k fine-grained, human-annotated preference comparison pairs. This dataset represents a substantial advancement over existing resources, offering superior size, diversity, annotation granularity, and quality. Leveraging this dataset, we propose several key innovations to improve both the quality of reward models and the efficiency of alignment algorithms. Notably, we introduce a Critique-Based Reward Model, which generates critiques of model outputs before assigning scores, offering enhanced interpretability and more informative feedback compared to traditional scalar reward mechanisms. Additionally, we propose Dynamic Reward Scaling, a method that adjusts the loss weight of each sample according to the reward signal, thereby optimizing the use of high-quality comparison pairs. Our approach is rigorously evaluated across 10 distinct dimensions and 27 benchmarks, with results demonstrating significant and consistent improvements in model performance. Specifically, fine-tuning LLaVA-ov-7B with MM-RLHF and our alignment algorithm leads to a 19.5% increase in conversational abilities and a 60% improvement in safety. We have open-sourced the preference dataset, reward model, training and evaluation code, as well as reward modeling and safety benchmarks. For more details, please visit our project page: https://mm-rlhf.github.io.

Most algorithms in reinforcement learning (RL) require that the objective is formalised with a Markovian reward function. However, it is well-known that certain tasks cannot be expressed by means of an objective in the Markov rewards formalism, motivating the study of alternative objective-specification formalisms in RL such as Linear Temporal Logic and Multi-Objective Reinforcement Learning. To date, there has not yet been any thorough analysis of how these formalisms relate to each other in terms of their expressivity. We fill this gap in the existing literature by providing a comprehensive comparison of 17 salient objective-specification formalisms. We place these formalisms in a preorder based on their expressive power, and present this preorder as a Hasse diagram. We find a variety of limitations for the different formalisms, and argue that no formalism is both dominantly expressive and straightforward to optimise with current techniques. For example, we prove that each of Regularised RL, (Outer) Nonlinear Markov Rewards, Reward Machines, Linear Temporal Logic, and Limit Average Rewards can express a task that the others cannot. The significance of our results is twofold. First, we identify important expressivity limitations to consider when specifying objectives for policy optimization. Second, our results highlight the need for future research which adapts reward learning to work with a greater variety of formalisms, since many existing reward learning methods assume that the desired objective takes a Markovian form. Our work contributes towards a more cohesive understanding of the costs and benefits of different RL objective-specification formalisms.

Reward finetuning has emerged as a promising approach to aligning foundation models with downstream objectives. Remarkable success has been achieved in the language domain by using reinforcement learning (RL) to maximize rewards that reflect human preference. However, in the vision domain, existing RL-based reward finetuning methods are limited by their instability in large-scale training, rendering them incapable of generalizing to complex, unseen prompts. In this paper, we propose Proximal Reward Difference Prediction (PRDP), enabling stable black-box reward finetuning for diffusion models for the first time on large-scale prompt datasets with over 100K prompts. Our key innovation is the Reward Difference Prediction (RDP) objective that has the same optimal solution as the RL objective while enjoying better training stability. Specifically, the RDP objective is a supervised regression objective that tasks the diffusion model with predicting the reward difference of generated image pairs from their denoising trajectories. We theoretically prove that the diffusion model that obtains perfect reward difference prediction is exactly the maximizer of the RL objective. We further develop an online algorithm with proximal updates to stably optimize the RDP objective. In experiments, we demonstrate that PRDP can match the reward maximization ability of well-established RL-based methods in small-scale training. Furthermore, through large-scale training on text prompts from the Human Preference Dataset v2 and the Pick-a-Pic v1 dataset, PRDP achieves superior generation quality on a diverse set of complex, unseen prompts whereas RL-based methods completely fail.

The success of Reinforcement Learning from Human Feedback (RLHF) critically depends on the quality of the reward model. While this quality is primarily evaluated through accuracy, it remains unclear whether accuracy fully captures what makes a reward model an effective teacher. We address this question from an optimization perspective. First, we prove that regardless of how accurate a reward model is, if it induces low reward variance, then the RLHF objective suffers from a flat landscape. Consequently, even a perfectly accurate reward model can lead to extremely slow optimization, underperforming less accurate models that induce higher reward variance. We additionally show that a reward model that works well for one language model can induce low reward variance, and thus a flat objective landscape, for another. These results establish a fundamental limitation of evaluating reward models solely based on accuracy or independently of the language model they guide. Experiments using models of up to 8B parameters corroborate our theory, demonstrating the interplay between reward variance, accuracy, and reward maximization rate. Overall, our findings highlight that beyond accuracy, a reward model needs to induce sufficient variance for efficient optimization.

Reinforcement learning (RL) has been widely adopted in post-training for large language models (LLMs) at scale. Recently, the incentivization of reasoning capabilities in LLMs from RL indicates that proper learning methods could enable effective inference-time scalability. A key challenge of RL is to obtain accurate reward signals for LLMs in various domains beyond verifiable questions or artificial rules. In this work, we investigate how to improve reward modeling (RM) with more inference compute for general queries, i.e. the inference-time scalability of generalist RM, and further, how to improve the effectiveness of performance-compute scaling with proper learning methods. For the RM approach, we adopt pointwise generative reward modeling (GRM) to enable flexibility for different input types and potential for inference-time scaling. For the learning method, we propose Self-Principled Critique Tuning (SPCT) to foster scalable reward generation behaviors in GRMs through online RL, to generate principles adaptively and critiques accurately, resulting in DeepSeek-GRM models. Furthermore, for effective inference-time scaling, we use parallel sampling to expand compute usage, and introduce a meta RM to guide voting process for better scaling performance. Empirically, we show that SPCT significantly improves the quality and scalability of GRMs, outperforming existing methods and models in various RM benchmarks without severe biases, and could achieve better performance compared to training-time scaling. DeepSeek-GRM still meets challenges in some tasks, which we believe can be addressed by future efforts in generalist reward systems. The models will be released and open-sourced.

Reinforcement learning algorithms typically struggle in the absence of a dense, well-shaped reward function. Intrinsically motivated exploration methods address this limitation by rewarding agents for visiting novel states or transitions, but these methods offer limited benefits in large environments where most discovered novelty is irrelevant for downstream tasks. We describe a method that uses background knowledge from text corpora to shape exploration. This method, called ELLM (Exploring with LLMs) rewards an agent for achieving goals suggested by a language model prompted with a description of the agent's current state. By leveraging large-scale language model pretraining, ELLM guides agents toward human-meaningful and plausibly useful behaviors without requiring a human in the loop. We evaluate ELLM in the Crafter game environment and the Housekeep robotic simulator, showing that ELLM-trained agents have better coverage of common-sense behaviors during pretraining and usually match or improve performance on a range of downstream tasks.

Foundation models are first pre-trained on vast unsupervised datasets and then fine-tuned on labeled data. Reinforcement learning, notably from human feedback (RLHF), can further align the network with the intended usage. Yet the imperfections in the proxy reward may hinder the training and lead to suboptimal results; the diversity of objectives in real-world tasks and human opinions exacerbate the issue. This paper proposes embracing the heterogeneity of diverse rewards by following a multi-policy strategy. Rather than focusing on a single a priori reward, we aim for Pareto-optimal generalization across the entire space of preferences. To this end, we propose rewarded soup, first specializing multiple networks independently (one for each proxy reward) and then interpolating their weights linearly. This succeeds empirically because we show that the weights remain linearly connected when fine-tuned on diverse rewards from a shared pre-trained initialization. We demonstrate the effectiveness of our approach for text-to-text (summarization, Q&A, helpful assistant, review), text-image (image captioning, text-to-image generation, visual grounding, VQA), and control (locomotion) tasks. We hope to enhance the alignment of deep models, and how they interact with the world in all its diversity.

Preference based Reinforcement Learning (PbRL) removes the need to hand specify a reward function by learning a reward from preference feedback over policy behaviors. Current approaches to PbRL do not address the credit assignment problem inherent in determining which parts of a behavior most contributed to a preference, which result in data intensive approaches and subpar reward functions. We address such limitations by introducing a credit assignment strategy (Hindsight PRIOR) that uses a world model to approximate state importance within a trajectory and then guides rewards to be proportional to state importance through an auxiliary predicted return redistribution objective. Incorporating state importance into reward learning improves the speed of policy learning, overall policy performance, and reward recovery on both locomotion and manipulation tasks. For example, Hindsight PRIOR recovers on average significantly (p<0.05) more reward on MetaWorld (20%) and DMC (15%). The performance gains and our ablations demonstrate the benefits even a simple credit assignment strategy can have on reward learning and that state importance in forward dynamics prediction is a strong proxy for a state's contribution to a preference decision. Code repository can be found at https://github.com/apple/ml-rlhf-hindsight-prior.

Personalizing large language models (LLMs) to accommodate diverse user preferences is essential for enhancing alignment and user satisfaction. Traditional reinforcement learning from human feedback (RLHF) approaches often rely on monolithic value representations, limiting their ability to adapt to individual preferences. We introduce a novel framework that leverages low-rank preference modeling to efficiently learn and generalize user-specific reward functions. By representing reward functions in a low-dimensional subspace and modeling individual preferences as weighted combinations of shared basis functions, our approach avoids rigid user categorization while enabling scalability and few-shot adaptation. We validate our method on multiple preference datasets, demonstrating superior generalization to unseen users and improved accuracy in preference prediction tasks.

In aligning large language models (LLMs), reward models have played an important role, but are standardly trained as discriminative models and rely only on labeled human preference data. In this paper, we explore methods that train reward models using both unlabeled and labeled data. Building on the generative models in LLMs, we develop a generative reward model that is first trained via large-scale unsupervised learning and then fine-tuned via supervised learning. We also show that by using label smoothing, we are in fact optimizing a regularized pairwise ranking loss. This result, in turn, provides a new view of training reward models, which links generative models and discriminative models under the same class of training objectives. The outcome of these techniques is a foundation reward model, which can be applied to a wide range of tasks with little or no further fine-tuning effort. Extensive experiments show that this model generalizes well across several tasks, including response ranking, reinforcement learning from human feedback, and task adaptation with fine-tuning, achieving significant performance improvements over several strong baseline models.

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward g(gamma, v) depends on the proposed threshold gamma and latent value v and it can be only achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most epsilon smaller than the optimum and prove that the number of queries needed can be infinitely large even when g(gamma, v) is monotone with respect to both gamma and v. On the positive side, we provide a tight query complexity Theta(1/epsilon^3) when g is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight Theta(1/epsilon^3) query complexity can be achieved as long as g satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight Theta(T^{2/3}) regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.

Extending Reinforcement Learning with Verifiable Rewards (RLVR) to real-world tasks often requires balancing objective and subjective evaluation criteria. However, many such tasks lack a single, unambiguous ground truth-making it difficult to define reliable reward signals for post-training language models. While traditional preference-based methods offer a workaround, they rely on opaque reward functions that are difficult to interpret and prone to spurious correlations. We introduce Rubrics as Rewards (RaR), a framework that uses structured, checklist-style rubrics as interpretable reward signals for on-policy training with GRPO. Our best RaR method yields up to a 28% relative improvement on HealthBench-1k compared to simple Likert-based approaches, while matching or surpassing the performance of reward signals derived from expert-written references. By treating rubrics as structured reward signals, we show that RaR enables smaller-scale judge models to better align with human preferences and sustain robust performance across model scales.

Recent work has shown that deep reinforcement learning agents have difficulty in effectively using their network parameters. We leverage prior insights into the advantages of sparse training techniques and demonstrate that gradual magnitude pruning enables agents to maximize parameter effectiveness. This results in networks that yield dramatic performance improvements over traditional networks and exhibit a type of "scaling law", using only a small fraction of the full network parameters.

Reward modeling in large language models is susceptible to reward hacking, causing models to latch onto superficial features such as the tendency to generate lists or unnecessarily long responses. In reinforcement learning from human feedback (RLHF) and more generally during post-training flawed reward signals often lead to outputs that optimize for these spurious correlates instead of genuine quality or correctness. We propose Context-Aware Reward Modeling (CARMO), a novel approach that first generates dynamic, context-relevant criteria to ground the reward model before producing reward scores. Unlike prior methods that rely on static rubrics, CARMO leverages large language models (LLMs) to adaptively create evaluation criteria such as logical consistency, clarity, and depth tailored to the user query. Our theoretical analysis shows that such criteria generation can mitigate reward hacking. We further demonstrate that CARMO can be distilled into smaller models, reducing the computational cost of alignment. We establish a new state-of-the-art performance in zero-shot settings for generative models, achieving a 2.1\% improvement on Reward Bench. Furthermore, alignment performed on the CARMO-curated preference dataset achieves 22.5\% and 21.1\% LC-WR and WR, respectively, on Mistral-Base (7B).

Large language models (LLMs) have enabled agents to perform complex reasoning and decision-making through free-form language interactions. However, in open-ended language action environments (e.g., negotiation or question-asking games), the action space can be formulated as a joint distribution over tokens, resulting in an exponentially large action space. Sampling actions in such a space can lead to extreme reward sparsity, which brings large reward variance, hindering effective reinforcement learning (RL). To address this, we propose ARIA, a method that Aggregates Rewards in Intention space to enable efficient and effective language Agents training. ARIA aims to project natural language actions from the high-dimensional joint token distribution space into a low-dimensional intention space, where semantically similar actions are clustered and assigned shared rewards. This intention-aware reward aggregation reduces reward variance by densifying reward signals, fostering better policy optimization. Extensive experiments demonstrate that ARIA not only significantly reduces policy gradient variance, but also delivers substantial performance gains of an average of 9.95% across four downstream tasks, consistently outperforming offline and online RL baselines.

Reward Models, essential for guiding Large Language Model optimization, are typically trained on fixed preference datasets, resulting in rigid alignment to single, implicit preference distributions. This prevents adaptation to diverse real-world needs-from conciseness in one task to detailed explanations in another. The standard practice of collecting task-specific preference data and retraining reward models is resource-intensive, often producing biased rewards, and limits practical application. We introduce generalizable, principle-following reward models. We propose that RMs should understand and adhere to dynamically provided natural language specifications of reward principles, similar to instruction-following in LLMs. To measure this capability, we develop RABench, a comprehensive benchmark for RMs focusing on generalization across diverse principles. Evaluations on RABench reveal poor generalization of current RMs. As a solution, we present RewardAnything, a novel RM designed and trained to explicitly follow natural language principles. We achieve SotA performance with RewardAnything in traditional RM benchmark simply by specifying a well-defined principle, and results on RABench show we excel in adapting to novel principles without retraining. Furthermore, RewardAnything integrates seamlessly with existing RLHF methods and we show by a case study on how to automatically and efficiently align LLMs with only natural language principles.