Daily Papers

We study the problem of learning a Nash equilibrium (NE) in an imperfect information game (IIG) through self-play. Precisely, we focus on two-player, zero-sum, episodic, tabular IIG under the perfect-recall assumption where the only feedback is realizations of the game (bandit feedback). In particular, the dynamic of the IIG is not known -- we can only access it by sampling or interacting with a game simulator. For this learning setting, we provide the Implicit Exploration Online Mirror Descent (IXOMD) algorithm. It is a model-free algorithm with a high-probability bound on the convergence rate to the NE of order 1/T where T is the number of played games. Moreover, IXOMD is computationally efficient as it needs to perform the updates only along the sampled trajectory.

We propose a new class of online learning algorithms, generalized implicit Follow-The-Regularized-Leader (FTRL), that expands the scope of FTRL framework. Generalized implicit FTRL can recover known algorithms, as FTRL with linearized losses and implicit FTRL, and it allows the design of new update rules, as extensions of aProx and Mirror-Prox to FTRL. Our theory is constructive in the sense that it provides a simple unifying framework to design updates that directly improve the worst-case upper bound on the regret. The key idea is substituting the linearization of the losses with a Fenchel-Young inequality. We show the flexibility of the framework by proving that some known algorithms, like the Mirror-Prox updates, are instantiations of the generalized implicit FTRL. Finally, the new framework allows us to recover the temporal variation bound of implicit OMD, with the same computational complexity.

We propose Banker Online Mirror Descent (Banker-OMD), a novel framework generalizing the classical Online Mirror Descent (OMD) technique in the online learning literature. The Banker-OMD framework almost completely decouples feedback delay handling and the task-specific OMD algorithm design, thus facilitating the design of new algorithms capable of efficiently and robustly handling feedback delays. Specifically, it offers a general methodology for achieving mathcal O(T + D)-style regret bounds in online bandit learning tasks with delayed feedback, where T is the number of rounds and D is the total feedback delay. We demonstrate the power of Banker-OMD by applications to two important bandit learning scenarios with delayed feedback, including delayed scale-free adversarial Multi-Armed Bandits (MAB) and delayed adversarial linear bandits. Banker-OMD leads to the first delayed scale-free adversarial MAB algorithm achieving mathcal O(KL(sqrt T+sqrt D)) regret and the first delayed adversarial linear bandit algorithm achieving mathcal O(poly(n)(T + D)) regret. As a corollary, the first application also implies mathcal O(KTL) regret for non-delayed scale-free adversarial MABs, which is the first to match the Omega(KTL) lower bound up to logarithmic factors and can be of independent interest.

Mirror descent (MD), a well-known first-order method in constrained convex optimization, has recently been shown as an important tool to analyze trust-region algorithms in reinforcement learning (RL). However, there remains a considerable gap between such theoretically analyzed algorithms and the ones used in practice. Inspired by this, we propose an efficient RL algorithm, called {\em mirror descent policy optimization} (MDPO). MDPO iteratively updates the policy by {\em approximately} solving a trust-region problem, whose objective function consists of two terms: a linearization of the standard RL objective and a proximity term that restricts two consecutive policies to be close to each other. Each update performs this approximation by taking multiple gradient steps on this objective function. We derive {\em on-policy} and {\em off-policy} variants of MDPO, while emphasizing important design choices motivated by the existing theory of MD in RL. We highlight the connections between on-policy MDPO and two popular trust-region RL algorithms: TRPO and PPO, and show that explicitly enforcing the trust-region constraint is in fact {\em not} a necessity for high performance gains in TRPO. We then show how the popular soft actor-critic (SAC) algorithm can be derived by slight modifications of off-policy MDPO. Overall, MDPO is derived from the MD principles, offers a unified approach to viewing a number of popular RL algorithms, and performs better than or on-par with TRPO, PPO, and SAC in a number of continuous control tasks. Code is available at https://github.com/manantomar/Mirror-Descent-Policy-Optimization.

Traditional Reinforcement Learning from Human Feedback (RLHF) often relies on reward models, frequently assuming preference structures like the Bradley-Terry model, which may not accurately capture the complexities of real human preferences (e.g., intransitivity). Nash Learning from Human Feedback (NLHF) offers a more direct alternative by framing the problem as finding a Nash equilibrium of a game defined by these preferences. In this work, we introduce Nash Mirror Prox (Nash-MP), an online NLHF algorithm that leverages the Mirror Prox optimization scheme to achieve fast and stable convergence to the Nash equilibrium. Our theoretical analysis establishes that Nash-MP exhibits last-iterate linear convergence towards the beta-regularized Nash equilibrium. Specifically, we prove that the KL-divergence to the optimal policy decreases at a rate of order (1+2beta)^{-N/2}, where N is a number of preference queries. We further demonstrate last-iterate linear convergence for the exploitability gap and uniformly for the span semi-norm of log-probabilities, with all these rates being independent of the size of the action space. Furthermore, we propose and analyze an approximate version of Nash-MP where proximal steps are estimated using stochastic policy gradients, making the algorithm closer to applications. Finally, we detail a practical implementation strategy for fine-tuning large language models and present experiments that demonstrate its competitive performance and compatibility with existing methods.

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an varepsilon-optimal policy with probability 1-delta under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings.

Reinforcement learning from human feedback (RLHF) has demonstrated remarkable effectiveness in aligning large language models (LLMs) with human preferences. Many existing alignment approaches rely on the Bradley-Terry (BT) model assumption, which assumes the existence of a ground-truth reward for each prompt-response pair. However, this assumption can be overly restrictive when modeling complex human preferences. In this paper, we drop the BT model assumption and study LLM alignment under general preferences, formulated as a two-player game. Drawing on theoretical insights from learning in games, we integrate optimistic online mirror descent into our alignment framework to approximate the Nash policy. Theoretically, we demonstrate that our approach achieves an O(T^{-1}) bound on the duality gap, improving upon the previous O(T^{-1/2}) result. More importantly, we implement our method and show through experiments that it outperforms state-of-the-art RLHF algorithms across multiple representative benchmarks.

Direct Preference Optimization (DPO) has emerged as a lightweight and effective alternative to Reinforcement Learning from Human Feedback (RLHF) and Reinforcement Learning with AI Feedback (RLAIF) for aligning large language and vision-language models. However, the standard DPO formulation, in which both the chosen and rejected responses are generated by the same policy, suffers from a weak learning signal because the two responses often share similar errors and exhibit small Kullback-Leibler (KL) divergence. This leads to slow and unstable convergence. To address this limitation, we introduce Reflective Preference Optimization (RPO), a new framework that incorporates hint-guided reflection into the DPO paradigm. RPO uses external models to identify hallucination sources and generate concise reflective hints, enabling the construction of on-policy preference pairs with stronger contrastiveness and clearer preference signals. We theoretically show that conditioning on hints increases the expected preference margin through mutual information and improves sample efficiency while remaining within the policy distribution family. Empirically, RPO achieves superior alignment with fewer training samples and iterations, substantially reducing hallucination rates and delivering state-of-the-art performance across multimodal benchmarks.

Stochastically Extended Adversarial (SEA) model is introduced by Sachs et al. [2022] as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition, they demonstrate that the expected regret of optimistic follow-the-regularized-leader (FTRL) depends on the cumulative stochastic variance sigma_{1:T}^2 and the cumulative adversarial variation Sigma_{1:T}^2 for convex functions. They also provide a slightly weaker bound based on the maximal stochastic variance sigma_{max}^2 and the maximal adversarial variation Sigma_{max}^2 for strongly convex functions. Inspired by their work, we investigate the theoretical guarantees of optimistic online mirror descent (OMD) for the SEA model. For convex and smooth functions, we obtain the same O(sigma_{1:T^2}+Sigma_{1:T^2}) regret bound, without the convexity requirement of individual functions. For strongly convex and smooth functions, we establish an O(min{log (sigma_{1:T}^2+Sigma_{1:T}^2), (sigma_{max}^2 + Sigma_{max}^2) log T}) bound, better than their O((sigma_{max}^2 + Sigma_{max}^2) log T) bound. For exp-concave and smooth functions, we achieve a new O(dlog(sigma_{1:T}^2+Sigma_{1:T}^2)) bound. Owing to the OMD framework, we can further extend our result to obtain dynamic regret guarantees, which are more favorable in non-stationary online scenarios. The attained results allow us to recover excess risk bounds of the stochastic setting and regret bounds of the adversarial setting, and derive new guarantees for many intermediate scenarios.

We study how to learn ε-optimal strategies in zero-sum imperfect information games (IIG) with trajectory feedback. In this setting, players update their policies sequentially based on their observations over a fixed number of episodes, denoted by T. Existing procedures suffer from high variance due to the use of importance sampling over sequences of actions (Steinberger et al., 2020; McAleer et al., 2022). To reduce this variance, we consider a fixed sampling approach, where players still update their policies over time, but with observations obtained through a given fixed sampling policy. Our approach is based on an adaptive Online Mirror Descent (OMD) algorithm that applies OMD locally to each information set, using individually decreasing learning rates and a regularized loss. We show that this approach guarantees a convergence rate of mathcal{O}(T^{-1/2}) with high probability and has a near-optimal dependence on the game parameters when applied with the best theoretical choices of learning rates and sampling policies. To achieve these results, we generalize the notion of OMD stabilization, allowing for time-varying regularization with convex increments.

The process of revising (or constructing) a policy at execution time -- known as decision-time planning -- has been key to achieving superhuman performance in perfect-information games like chess and Go. A recent line of work has extended decision-time planning to imperfect-information games, leading to superhuman performance in poker. However, these methods involve solving subgames whose sizes grow quickly in the amount of non-public information, making them unhelpful when the amount of non-public information is large. Motivated by this issue, we introduce an alternative framework for decision-time planning that is not based on solving subgames, but rather on update equivalence. In this update-equivalence framework, decision-time planning algorithms replicate the updates of last-iterate algorithms, which need not rely on public information. This facilitates scalability to games with large amounts of non-public information. Using this framework, we derive a provably sound search algorithm for fully cooperative games based on mirror descent and a search algorithm for adversarial games based on magnetic mirror descent. We validate the performance of these algorithms in cooperative and adversarial domains, notably in Hanabi, the standard benchmark for search in fully cooperative imperfect-information games. Here, our mirror descent approach exceeds or matches the performance of public information-based search while using two orders of magnitude less search time. This is the first instance of a non-public-information-based algorithm outperforming public-information-based approaches in a domain they have historically dominated.

This paper studies the theoretical framework of the alignment process of generative models with Reinforcement Learning from Human Feedback (RLHF). We consider a standard mathematical formulation, the reverse-KL regularized contextual bandit for RLHF. Despite its widespread practical application, a rigorous theoretical analysis of this formulation remains open. We investigate its behavior in three distinct settings -- offline, online, and hybrid -- and propose efficient algorithms with finite-sample theoretical guarantees. Moving towards practical applications, our framework, with a robust approximation of the information-theoretical policy improvement oracle, naturally gives rise to several novel RLHF algorithms. This includes an iterative version of the Direct Preference Optimization (DPO) algorithm for online settings, and a multi-step rejection sampling strategy for offline scenarios. Our empirical evaluations on real-world alignment experiment of large language model demonstrate that these proposed methods significantly surpass existing strong baselines, such as DPO and Rejection Sampling Optimization (RSO), showcasing the connections between solid theoretical foundations and their powerful practical implementations.

In Reinforcement Learning (RL), regularization has emerged as a popular tool both in theory and practice, typically based either on an entropy bonus or a Kullback-Leibler divergence that constrains successive policies. In practice, these approaches have been shown to improve exploration, robustness and stability, giving rise to popular Deep RL algorithms such as SAC and TRPO. Policy Mirror Descent (PMD) is a theoretical framework that solves this general regularized policy optimization problem, however the closed-form solution involves the sum of all past Q-functions, which is intractable in practice. We propose and analyze PMD-like algorithms that only keep the last M Q-functions in memory, and show that for finite and large enough M, a convergent algorithm can be derived, introducing no error in the policy update, unlike prior deep RL PMD implementations. StaQ, the resulting algorithm, enjoys strong theoretical guarantees and is competitive with deep RL baselines, while exhibiting less performance oscillation, paving the way for fully stable deep RL algorithms and providing a testbed for experimentation with Policy Mirror Descent.

We address the challenge of online Reinforcement Learning from Human Feedback (RLHF) with a focus on self-rewarding alignment methods. In online RLHF, obtaining feedback requires interaction with the environment, which can be costly when using additional reward models or the GPT-4 API. Current self-rewarding approaches rely heavily on the discriminator's judgment capabilities, which are effective for large-scale models but challenging to transfer to smaller ones. To address these limitations, we propose a novel, only-prompting self-rewarding online algorithm that generates preference datasets without relying on judgment capabilities. Additionally, we employ fine-grained arithmetic control over the optimality gap between positive and negative examples, generating more hard negatives in the later stages of training to help the model better capture subtle human preferences. Finally, we conduct extensive experiments on two base models, Mistral-7B and Mistral-Instruct-7B, which significantly bootstrap the performance of the reference model, achieving 34.5% in the Length-controlled Win Rates of AlpacaEval 2.0.

The last decade has witnessed many successes of deep learning-based models for industry-scale recommender systems. These models are typically trained offline in a batch manner. While being effective in capturing users' past interactions with recommendation platforms, batch learning suffers from long model-update latency and is vulnerable to system biases, making it hard to adapt to distribution shift and explore new items or user interests. Although online learning-based approaches (e.g., multi-armed bandits) have demonstrated promising theoretical results in tackling these challenges, their practical real-time implementation in large-scale recommender systems remains limited. First, the scalability of online approaches in servicing a massive online traffic while ensuring timely updates of bandit parameters poses a significant challenge. Additionally, exploring uncertainty in recommender systems can easily result in unfavorable user experience, highlighting the need for devising intricate strategies that effectively balance the trade-off between exploitation and exploration. In this paper, we introduce Online Matching: a scalable closed-loop bandit system learning from users' direct feedback on items in real time. We present a hybrid "offline + online" approach for constructing this system, accompanied by a comprehensive exposition of the end-to-end system architecture. We propose Diag-LinUCB -- a novel extension of the LinUCB algorithm -- to enable distributed updates of bandits parameter in a scalable and timely manner. We conduct live experiments in YouTube and show that Online Matching is able to enhance the capabilities of fresh content discovery and item exploration in the present platform.

Despite strong generalization capabilities, Vision-Language-Action (VLA) models remain constrained by the high cost of expert demonstrations and insufficient real-world interaction. While online reinforcement learning (RL) has shown promise in improving general foundation models, applying RL to VLA manipulation in real-world settings is still hindered by low exploration efficiency and a restricted exploration space. Through systematic real-world experiments, we observe that the effective exploration space of online RL is closely tied to the data distribution of supervised fine-tuning (SFT). Motivated by this observation, we propose TwinRL, a digital twin-real-world collaborative RL framework designed to scale and guide exploration for VLA models. First, a high-fidelity digital twin is efficiently reconstructed from smartphone-captured scenes, enabling realistic bidirectional transfer between real and simulated environments. During the SFT warm-up stage, we introduce an exploration space expansion strategy using digital twins to broaden the support of the data trajectory distribution. Building on this enhanced initialization, we propose a sim-to-real guided exploration strategy to further accelerate online RL. Specifically, TwinRL performs efficient and parallel online RL in the digital twin prior to deployment, effectively bridging the gap between offline and online training stages. Subsequently, we exploit efficient digital twin sampling to identify failure-prone yet informative configurations, which are used to guide targeted human-in-the-loop rollouts on the real robot. In our experiments, TwinRL approaches 100% success in both in-distribution regions covered by real-world demonstrations and out-of-distribution regions, delivering at least a 30% speedup over prior real-world RL methods and requiring only about 20 minutes on average across four tasks.

We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a regularized mirror map that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-t prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-t priors and primal-space guarantees for constrained generation, under varepsilon-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks.

In this paper, we present ContExtual Imitation Learning~(CEIL), a general and broadly applicable algorithm for imitation learning (IL). Inspired by the formulation of hindsight information matching, we derive CEIL by explicitly learning a hindsight embedding function together with a contextual policy using the hindsight embeddings. To achieve the expert matching objective for IL, we advocate for optimizing a contextual variable such that it biases the contextual policy towards mimicking expert behaviors. Beyond the typical learning from demonstrations (LfD) setting, CEIL is a generalist that can be effectively applied to multiple settings including: 1)~learning from observations (LfO), 2)~offline IL, 3)~cross-domain IL (mismatched experts), and 4) one-shot IL settings. Empirically, we evaluate CEIL on the popular MuJoCo tasks (online) and the D4RL dataset (offline). Compared to prior state-of-the-art baselines, we show that CEIL is more sample-efficient in most online IL tasks and achieves better or competitive performances in offline tasks.

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.

Policy mirror descent (PMD) provides a principled framework for reinforcement learning (RL) by iteratively solving KL-regularized policy improvement subproblems. While this approach has been adopted in training advanced LLMs such as Kimi K1.5/K2, the ideal closed-form PMD updates require reliable partition function estimation, a significant challenge when working with limited rollouts in the vast action spaces of LLMs. We investigate a practical algorithm, termed PMD-mean, that approximates the log-partition term with the mean reward under the sampling policy and performs regression in log-policy space. Specifically, we characterize the population solution of PMD-mean and demonstrate that it implicitly optimizes mirror descent subproblems with an adaptive mixed KL--χ^2 regularizer. This additional χ^2 regularization constrains large probability changes, producing more conservative updates when expected rewards are low and enhancing robustness against finite-sample estimation errors. Experiments on math reasoning tasks show that PMD-mean achieves superior performance with improved stability and time efficiency. These findings deepen our understanding of PMD-mean and illuminate pathways toward principled improvements in RL algorithms for LLMs. Code is available at https://github.com/horizon-rl/OpenKimi.

We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions.We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses.Our algorithm obtains an widetilde O(K^{6/7}) regret bound, improving significantly over previous state-of-the-art of widetilde O (K^{14/15}) in this setting. In addition, we present a version of the same algorithm under the assumption a simulator of the environment is available to the learner (but otherwise no exploratory assumptions are made), and prove it obtains state-of-the-art regret of widetilde O (K^{2/3}).

The goal of reinforcement learning (RL) is to find a policy that maximizes the expected cumulative return. It has been shown that this objective can be represented as an optimization problem of state-action visitation distribution under linear constraints. The dual problem of this formulation, which we refer to as dual RL, is unconstrained and easier to optimize. In this work, we first cast several state-of-the-art offline RL and offline imitation learning (IL) algorithms as instances of dual RL approaches with shared structures. Such unification allows us to identify the root cause of the shortcomings of prior methods. For offline IL, our analysis shows that prior methods are based on a restrictive coverage assumption that greatly limits their performance in practice. To fix this limitation, we propose a new discriminator-free method ReCOIL that learns to imitate from arbitrary off-policy data to obtain near-expert performance. For offline RL, our analysis frames a recent offline RL method XQL in the dual framework, and we further propose a new method f-DVL that provides alternative choices to the Gumbel regression loss that fixes the known training instability issue of XQL. The performance improvements by both of our proposed methods, ReCOIL and f-DVL, in IL and RL are validated on an extensive suite of simulated robot locomotion and manipulation tasks. Project code and details can be found at this https://hari-sikchi.github.io/dual-rl.

In this work, we consider and analyze the sample complexity of model-free reinforcement learning with a generative model. Particularly, we analyze mirror descent value iteration (MDVI) by Geist et al. (2019) and Vieillard et al. (2020a), which uses the Kullback-Leibler divergence and entropy regularization in its value and policy updates. Our analysis shows that it is nearly minimax-optimal for finding an varepsilon-optimal policy when varepsilon is sufficiently small. This is the first theoretical result that demonstrates that a simple model-free algorithm without variance-reduction can be nearly minimax-optimal under the considered setting.

Reinforcement learning from human feedback (RLHF) has emerged as a central tool for language model alignment. We consider online exploration in RLHF, which exploits interactive access to human or AI feedback by deliberately encouraging the model to produce diverse, maximally informative responses. By allowing RLHF to confidently stray from the pre-trained model, online exploration offers the possibility of novel, potentially super-human capabilities, but its full potential as a paradigm for language model training has yet to be realized, owing to computational and statistical bottlenecks in directly adapting existing reinforcement learning techniques. We propose a new algorithm for online exploration in RLHF, Exploratory Preference Optimization (XPO), which is simple and practical -- a one-line change to (online) Direct Preference Optimization (DPO; Rafailov et al., 2023) -- yet enjoys the strongest known provable guarantees and promising empirical performance. XPO augments the DPO objective with a novel and principled exploration bonus, empowering the algorithm to explore outside the support of the initial model and human feedback data. In theory, we show that XPO is provably sample-efficient and converges to a near-optimal language model policy under natural exploration conditions, irrespective of whether the initial model has good coverage. Our analysis, which builds on the observation that DPO implicitly performs a form of Q^{star}-approximation (or, Bellman error minimization), combines previously disparate techniques from language modeling and theoretical reinforcement learning in a serendipitous fashion through the perspective of KL-regularized Markov decision processes. Empirically, we find that XPO is more sample-efficient than non-exploratory DPO variants in a preliminary evaluation.

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.

We propose iterative inversion -- an algorithm for learning an inverse function without input-output pairs, but only with samples from the desired output distribution and access to the forward function. The key challenge is a distribution shift between the desired outputs and the outputs of an initial random guess, and we prove that iterative inversion can steer the learning correctly, under rather strict conditions on the function. We apply iterative inversion to learn control. Our input is a set of demonstrations of desired behavior, given as video embeddings of trajectories (without actions), and our method iteratively learns to imitate trajectories generated by the current policy, perturbed by random exploration noise. Our approach does not require rewards, and only employs supervised learning, which can be easily scaled to use state-of-the-art trajectory embedding techniques and policy representations. Indeed, with a VQ-VAE embedding, and a transformer-based policy, we demonstrate non-trivial continuous control on several tasks. Further, we report an improved performance on imitating diverse behaviors compared to reward based methods.

Learning from human preference data has emerged as the dominant paradigm for fine-tuning large language models (LLMs). The two most common families of techniques -- online reinforcement learning (RL) such as Proximal Policy Optimization (PPO) and offline contrastive methods such as Direct Preference Optimization (DPO) -- were positioned as equivalent in prior work due to the fact that both have to start from the same offline preference dataset. To further expand our theoretical understanding of the similarities and differences between online and offline techniques for preference fine-tuning, we conduct a rigorous analysis through the lens of dataset coverage, a concept that captures how the training data covers the test distribution and is widely used in RL. We prove that a global coverage condition is both necessary and sufficient for offline contrastive methods to converge to the optimal policy, but a weaker partial coverage condition suffices for online RL methods. This separation provides one explanation of why online RL methods can perform better than offline methods, especially when the offline preference data is not diverse enough. Finally, motivated by our preceding theoretical observations, we derive a hybrid preference optimization (HyPO) algorithm that uses offline data for contrastive-based preference optimization and online data for KL regularization. Theoretically and empirically, we demonstrate that HyPO is more performant than its pure offline counterpart DPO, while still preserving its computation and memory efficiency.

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.

Learning from visual observation (LfVO), aiming at recovering policies from only visual observation data, is promising yet a challenging problem. Existing LfVO approaches either only adopt inefficient online learning schemes or require additional task-specific information like goal states, making them not suited for open-ended tasks. To address these issues, we propose a two-stage framework for learning from visual observation. In the first stage, we introduce and pretrain State-to-Go (STG) Transformer offline to predict and differentiate latent transitions of demonstrations. Subsequently, in the second stage, the STG Transformer provides intrinsic rewards for downstream reinforcement learning tasks where an agent learns merely from intrinsic rewards. Empirical results on Atari and Minecraft show that our proposed method outperforms baselines and in some tasks even achieves performance comparable to the policy learned from environmental rewards. These results shed light on the potential of utilizing video-only data to solve difficult visual reinforcement learning tasks rather than relying on complete offline datasets containing states, actions, and rewards. The project's website and code can be found at https://sites.google.com/view/stgtransformer.

Recent Large Language Models (LLMs) and Large Vision-Language Models (LVLMs) increasingly use Reinforcement Learning (RL) for post-pretraining, such as RL with Verifiable Rewards (RLVR) for objective tasks and RL from Human Feedback (RLHF) for subjective tasks. However, RLHF incurs high costs and potential reward-policy mismatch due to reliance on human preferences, while RLVR still wastes supervision by discarding rollouts and correctness signals after each update. To address these challenges, we introduce the Synergistic Policy And Reward Co-Evolving Framework (SPARK), an efficient, on-policy, and stable method that builds on RLVR. Instead of discarding rollouts and correctness data, SPARK recycles this valuable information to simultaneously train the model itself as a generative reward model. This auxiliary training uses a mix of objectives, such as pointwise reward score, pairwise comparison, and evaluation conditioned on further-reflection responses, to teach the model to evaluate and improve its own responses. Our process eliminates the need for a separate reward model and costly human preference data. SPARK creates a positive co-evolving feedback loop: improved reward accuracy yields better policy gradients, which in turn produce higher-quality rollouts that further refine the reward model. Our unified framework supports test-time scaling via self-reflection without external reward models and their associated costs. We show that SPARK achieves significant performance gains on multiple LLM and LVLM models and multiple reasoning, reward models, and general benchmarks. For example, SPARK-VL-7B achieves an average 9.7% gain on 7 reasoning benchmarks, 12.1% on 2 reward benchmarks, and 1.5% on 8 general benchmarks over the baselines, demonstrating robustness and broad generalization.

This paper introduces MR-Search, an in-context meta reinforcement learning (RL) formulation for agentic search with self-reflection. Instead of optimizing a policy within a single independent episode with sparse rewards, MR-Search trains a policy that conditions on past episodes and adapts its search strategy across episodes. MR-Search learns to learn a search strategy with self-reflection, allowing search agents to improve in-context exploration at test-time. Specifically, MR-Search performs cross-episode exploration by generating explicit self-reflections after each episode and leveraging them as additional context to guide subsequent attempts, thereby promoting more effective exploration during test-time. We further introduce a multi-turn RL algorithm that estimates a dense relative advantage at the turn level, enabling fine-grained credit assignment on each episode. Empirical results across various benchmarks demonstrate the advantages of MR-Search over baselines based RL, showing strong generalization and relative improvements of 9.2% to 19.3% across eight benchmarks. Our code and data are available at https://github.com/tengxiao1/MR-Search.

We study a new paradigm for sequential decision making, called offline Policy Learning from Observation (PLfO). Offline PLfO aims to learn policies using datasets with substandard qualities: 1) only a subset of trajectories is labeled with rewards, 2) labeled trajectories may not contain actions, 3) labeled trajectories may not be of high quality, and 4) the overall data may not have full coverage. Such imperfection is common in real-world learning scenarios, so offline PLfO encompasses many existing offline learning setups, including offline imitation learning (IL), ILfO, and reinforcement learning (RL). In this work, we present a generic approach, called Modality-agnostic Adversarial Hypothesis Adaptation for Learning from Observations (MAHALO), for offline PLfO. Built upon the pessimism concept in offline RL, MAHALO optimizes the policy using a performance lower bound that accounts for uncertainty due to the dataset's insufficient converge. We implement this idea by adversarially training data-consistent critic and reward functions in policy optimization, which forces the learned policy to be robust to the data deficiency. We show that MAHALO consistently outperforms or matches specialized algorithms across a variety of offline PLfO tasks in theory and experiments.

Preference-based feedback is important for many applications in machine learning where evaluation of a reward function is not feasible. Notable recent examples arise in preference alignment for large language models, including in reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO). For many applications of preference alignment, the cost of acquiring human feedback can be substantial. In this work, we take advantage of the fact that one can often choose contexts at which to obtain human feedback to most efficiently identify a good policy, and formalize the setting as an active contextual dueling bandit problem. We propose an active exploration algorithm to efficiently select the data and provide theoretical proof that it has a polynomial worst-case regret bound. We extend the setting and methodology for practical use in preference alignment of large language models. We provide two extensions, an online and an offline approach. Our method outperforms the baselines with limited samples of human preferences on several language models and four real-world datasets including two new datasets that we contribute to the literature.

The rapid development of large language and multimodal models has sparked significant interest in using proprietary models, such as GPT-4o, to develop autonomous agents capable of handling real-world scenarios like web navigation. Although recent open-source efforts have tried to equip agents with the ability to explore environments and continuously improve over time, they are building text-only agents in synthetic environments where the reward signals are clearly defined. Such agents struggle to generalize to realistic settings that require multimodal perception abilities and lack ground-truth signals. In this paper, we introduce an open-source framework designed to facilitate the development of multimodal web agent that can autonomously conduct real-world exploration and improve itself. We first train the base model with imitation learning to gain the basic abilities. We then let the agent explore the open web and collect feedback on its trajectories. After that, it further improves its policy by learning from well-performing trajectories judged by another general-purpose model. This exploration-feedback-optimization cycle can continue for several iterations. Experimental results show that our web agent successfully improves itself after each iteration, demonstrating strong performance across multiple test sets.

Selecting exploratory actions that generate a rich stream of experience for better learning is a fundamental challenge in reinforcement learning (RL). An approach to tackle this problem consists in selecting actions according to specific policies for an extended period of time, also known as options. A recent line of work to derive such exploratory options builds upon the eigenfunctions of the graph Laplacian. Importantly, until now these methods have been mostly limited to tabular domains where (1) the graph Laplacian matrix was either given or could be fully estimated, (2) performing eigendecomposition on this matrix was computationally tractable, and (3) value functions could be learned exactly. Additionally, these methods required a separate option discovery phase. These assumptions are fundamentally not scalable. In this paper we address these limitations and show how recent results for directly approximating the eigenfunctions of the Laplacian can be leveraged to truly scale up options-based exploration. To do so, we introduce a fully online deep RL algorithm for discovering Laplacian-based options and evaluate our approach on a variety of pixel-based tasks. We compare to several state-of-the-art exploration methods and show that our approach is effective, general, and especially promising in non-stationary settings.

Inverse Reinforcement Learning (IRL) is a powerful set of techniques for imitation learning that aims to learn a reward function that rationalizes expert demonstrations. Unfortunately, traditional IRL methods suffer from a computational weakness: they require repeatedly solving a hard reinforcement learning (RL) problem as a subroutine. This is counter-intuitive from the viewpoint of reductions: we have reduced the easier problem of imitation learning to repeatedly solving the harder problem of RL. Another thread of work has proved that access to the side-information of the distribution of states where a strong policy spends time can dramatically reduce the sample and computational complexities of solving an RL problem. In this work, we demonstrate for the first time a more informed imitation learning reduction where we utilize the state distribution of the expert to alleviate the global exploration component of the RL subroutine, providing an exponential speedup in theory. In practice, we find that we are able to significantly speed up the prior art on continuous control tasks.

Recently, a wide range of memory-efficient LLM training algorithms have gained substantial popularity. These methods leverage the low-rank structure of gradients to project optimizer states into a subspace using projection matrix found by singular value decomposition (SVD). However, convergence of these algorithms is highly dependent on the update rules of their projection matrix. In this work, we provide the first convergence guarantee for arbitrary update rules of projection matrix. This guarantee is generally applicable to optimizers that can be analyzed with Hamiltonian Descent, including most common ones, such as LION, Adam. Inspired by our theoretical understanding, we propose Online Subspace Descent, a new family of subspace descent optimizer without SVD. Instead of updating the projection matrix with eigenvectors, Online Subspace Descent updates the projection matrix with online PCA. Online Subspace Descent is flexible and introduces only minimum overhead to training. We show that for the task of pretraining LLaMA models ranging from 60M to 7B parameters on the C4 dataset, Online Subspace Descent achieves lower perplexity and better downstream tasks performance than state-of-the-art low-rank training methods across different settings and narrows the gap with full-rank baselines.

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.

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.

Despite the promise of RLHF in aligning LLMs with human preferences, it often leads to superficial alignment, prioritizing stylistic changes over improving downstream performance of LLMs. Underspecified preferences could obscure directions to align the models. Lacking exploration restricts identification of desirable outputs to improve the models. To overcome these challenges, we propose a novel framework: Reinforcement Learning from Reflective Feedback (RLRF), which leverages fine-grained feedback based on detailed criteria to improve the core capabilities of LLMs. RLRF employs a self-reflection mechanism to systematically explore and refine LLM responses, then fine-tuning the models via a RL algorithm along with promising responses. Our experiments across Just-Eval, Factuality, and Mathematical Reasoning demonstrate the efficacy and transformative potential of RLRF beyond superficial surface-level adjustment.

Reinforcement learning from human feedback (RLHF) has emerged as the main paradigm for aligning large language models (LLMs) with human preferences. Typically, RLHF involves the initial step of learning a reward model from human feedback, often expressed as preferences between pairs of text generations produced by a pre-trained LLM. Subsequently, the LLM's policy is fine-tuned by optimizing it to maximize the reward model through a reinforcement learning algorithm. However, an inherent limitation of current reward models is their inability to fully represent the richness of human preferences and their dependency on the sampling distribution. In this study, we introduce an alternative pipeline for the fine-tuning of LLMs using pairwise human feedback. Our approach entails the initial learning of a preference model, which is conditioned on two inputs given a prompt, followed by the pursuit of a policy that consistently generates responses preferred over those generated by any competing policy, thus defining the Nash equilibrium of this preference model. We term this approach Nash learning from human feedback (NLHF). In the context of a tabular policy representation, we present a novel algorithmic solution, Nash-MD, founded on the principles of mirror descent. This algorithm produces a sequence of policies, with the last iteration converging to the regularized Nash equilibrium. Additionally, we explore parametric representations of policies and introduce gradient descent algorithms for deep-learning architectures. To demonstrate the effectiveness of our approach, we present experimental results involving the fine-tuning of a LLM for a text summarization task. We believe NLHF offers a compelling avenue for preference learning and policy optimization with the potential of advancing the field of aligning LLMs with human preferences.

Fine-tuning diffusion models via online reinforcement learning (RL) has shown great potential for enhancing text-to-image alignment. However, since precisely specifying a ground-truth objective for visual tasks remains challenging, the models are often optimized using a proxy reward that only partially captures the true goal. This mismatch often leads to reward hacking, where proxy scores increase while real image quality deteriorates and generation diversity collapses. While common solutions add regularization against the reference policy to prevent reward hacking, they compromise sample efficiency and impede the exploration of novel, high-reward regions, as the reference policy is usually sub-optimal. To address the competing demands of sample efficiency, effective exploration, and mitigation of reward hacking, we propose Gated and Adaptive Regularization with Diversity-aware Optimization (GARDO), a versatile framework compatible with various RL algorithms. Our key insight is that regularization need not be applied universally; instead, it is highly effective to selectively penalize a subset of samples that exhibit high uncertainty. To address the exploration challenge, GARDO introduces an adaptive regularization mechanism wherein the reference model is periodically updated to match the capabilities of the online policy, ensuring a relevant regularization target. To address the mode collapse issue in RL, GARDO amplifies the rewards for high-quality samples that also exhibit high diversity, encouraging mode coverage without destabilizing the optimization process. Extensive experiments across diverse proxy rewards and hold-out unseen metrics consistently show that GARDO mitigates reward hacking and enhances generation diversity without sacrificing sample efficiency or exploration, highlighting its effectiveness and robustness.

Active Visual Exploration (AVE) is a task that involves dynamically selecting observations (glimpses), which is critical to facilitate comprehension and navigation within an environment. While modern AVE methods have demonstrated impressive performance, they are constrained to fixed-scale glimpses from rigid grids. In contrast, existing mobile platforms equipped with optical zoom capabilities can capture glimpses of arbitrary positions and scales. To address this gap between software and hardware capabilities, we introduce AdaGlimpse. It uses Soft Actor-Critic, a reinforcement learning algorithm tailored for exploration tasks, to select glimpses of arbitrary position and scale. This approach enables our model to rapidly establish a general awareness of the environment before zooming in for detailed analysis. Experimental results demonstrate that AdaGlimpse surpasses previous methods across various visual tasks while maintaining greater applicability in realistic AVE scenarios.

Humans often acquire new skills through observation and imitation. For robotic agents, learning from the plethora of unlabeled video demonstration data available on the Internet necessitates imitating the expert without access to its action, presenting a challenge known as Imitation Learning from Observations (ILfO). A common approach to tackle ILfO problems is to convert them into inverse reinforcement learning problems, utilizing a proxy reward computed from the agent's and the expert's observations. Nonetheless, we identify that tasks characterized by a progress dependency property pose significant challenges for such approaches; in these tasks, the agent needs to initially learn the expert's preceding behaviors before mastering the subsequent ones. Our investigation reveals that the main cause is that the reward signals assigned to later steps hinder the learning of initial behaviors. To address this challenge, we present a novel ILfO framework that enables the agent to master earlier behaviors before advancing to later ones. We introduce an Automatic Discount Scheduling (ADS) mechanism that adaptively alters the discount factor in reinforcement learning during the training phase, prioritizing earlier rewards initially and gradually engaging later rewards only when the earlier behaviors have been mastered. Our experiments, conducted on nine Meta-World tasks, demonstrate that our method significantly outperforms state-of-the-art methods across all tasks, including those that are unsolvable by them.

Post-training of flow matching models-aligning the output distribution with a high-quality target-is mathematically equivalent to imitation learning. While Supervised Fine-Tuning mimics expert demonstrations effectively, it cannot correct policy drift in unseen states. Preference optimization methods address this but require costly preference pairs or reward modeling. We propose Flow Matching Adversarial Imitation Learning (FAIL), which minimizes policy-expert divergence through adversarial training without explicit rewards or pairwise comparisons. We derive two algorithms: FAIL-PD exploits differentiable ODE solvers for low-variance pathwise gradients, while FAIL-PG provides a black-box alternative for discrete or computationally constrained settings. Fine-tuning FLUX with only 13,000 demonstrations from Nano Banana pro, FAIL achieves competitive performance on prompt following and aesthetic benchmarks. Furthermore, the framework generalizes effectively to discrete image and video generation, and functions as a robust regularizer to mitigate reward hacking in reward-based optimization. Code and data are available at https://github.com/HansPolo113/FAIL.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

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.

In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation, where consecutive plays of the same action lead to decreased performance, or deprivation, where the payoff of an action increases after an interval of inactivity. In this work, we take a step towards understanding the approximability of planning LSD bandits, namely, the (NP-hard) problem of computing an optimal arm-pulling strategy under complete knowledge of the model. In particular, we design the first efficient constant approximation algorithm for the problem and show that, under a natural monotonicity assumption on the payoffs, its approximation guarantee (almost) matches the state-of-the-art for the special and well-studied class of recharging bandits (also known as delay-dependent). In this attempt, we develop new tools and insights for this class of problems, including a novel higher-dimensional relaxation and the technique of mirroring the evolution of virtual states. We believe that these novel elements could potentially be used for approaching richer classes of action-induced nonstationary bandits (e.g., special instances of restless bandits). In the case where the model parameters are initially unknown, we develop an online learning adaptation of our algorithm for which we provide sublinear regret guarantees against its full-information counterpart.

In reinforcement learning (RL), there are two major settings for interacting with the environment: online and offline. Online methods explore the environment at significant time cost, and offline methods efficiently obtain reward signals by sacrificing exploration capability. We propose semi-offline RL, a novel paradigm that smoothly transits from offline to online settings, balances exploration capability and training cost, and provides a theoretical foundation for comparing different RL settings. Based on the semi-offline formulation, we present the RL setting that is optimal in terms of optimization cost, asymptotic error, and overfitting error bound. Extensive experiments show that our semi-offline approach is efficient and yields comparable or often better performance compared with state-of-the-art methods.

Reinforcement Learning with Verifiable Rewards (RLVR) has propelled Large Language Models in complex reasoning, yet its scalability is often hindered by a training bottleneck where performance plateaus as policy entropy collapses, signaling a loss of exploration. Previous methods typically address this by maintaining high policy entropy, yet the precise mechanisms that govern meaningful exploration have remained underexplored. Our analysis suggests that an unselective focus on entropy risks amplifying irrelevant tokens and destabilizing training. This paper investigates the exploration dynamics within RLVR and identifies a key issue: the gradual elimination of valuable low-probability exploratory tokens, which we term \textit{reasoning sparks}. We find that while abundant in pre-trained models, these sparks are systematically extinguished during RLVR due to over-penalization, leading to a degeneracy in exploration. To address this, we introduce Low-probability Regularization (Lp-Reg). Its core mechanism regularizes the policy towards a heuristic proxy distribution. This proxy is constructed by filtering out presumed noise tokens and re-normalizing the distribution over the remaining candidates. The result is a less-noisy proxy where the probability of reasoning sparks is amplified, which then serves as a soft regularization target to shield these valuable tokens from elimination via KL divergence. Experiments show that Lp-Reg enables stable on-policy training for around 1,000 steps, a regime where baseline entropy-control methods collapse. This sustained exploration leads to state-of-the-art performance, achieving a 60.17% average accuracy on five math benchmarks, an improvement of 2.66% over prior methods. Code is available at https://github.com/CarlanLark/Lp-Reg.

Recent advances in large vision-language models (LVLMs) have shown promise for embodied task planning, yet they struggle with fundamental challenges like dependency constraints and efficiency. Existing approaches either solely optimize action selection or leverage world models during inference, overlooking the benefits of learning to model the world as a way to enhance planning capabilities. We propose Dual Preference Optimization (D^2PO), a new learning framework that jointly optimizes state prediction and action selection through preference learning, enabling LVLMs to understand environment dynamics for better planning. To automatically collect trajectories and stepwise preference data without human annotation, we introduce a tree search mechanism for extensive exploration via trial-and-error. Extensive experiments on VoTa-Bench demonstrate that our D^2PO-based method significantly outperforms existing methods and GPT-4o when applied to Qwen2-VL (7B), LLaVA-1.6 (7B), and LLaMA-3.2 (11B), achieving superior task success rates with more efficient execution paths.

We present BYOL-Explore, a conceptually simple yet general approach for curiosity-driven exploration in visually-complex environments. BYOL-Explore learns a world representation, the world dynamics, and an exploration policy all-together by optimizing a single prediction loss in the latent space with no additional auxiliary objective. We show that BYOL-Explore is effective in DM-HARD-8, a challenging partially-observable continuous-action hard-exploration benchmark with visually-rich 3-D environments. On this benchmark, we solve the majority of the tasks purely through augmenting the extrinsic reward with BYOL-Explore s intrinsic reward, whereas prior work could only get off the ground with human demonstrations. As further evidence of the generality of BYOL-Explore, we show that it achieves superhuman performance on the ten hardest exploration games in Atari while having a much simpler design than other competitive agents.

We describe a robotic learning system for autonomous exploration and navigation in diverse, open-world environments. At the core of our method is a learned latent variable model of distances and actions, along with a non-parametric topological memory of images. We use an information bottleneck to regularize the learned policy, giving us (i) a compact visual representation of goals, (ii) improved generalization capabilities, and (iii) a mechanism for sampling feasible goals for exploration. Trained on a large offline dataset of prior experience, the model acquires a representation of visual goals that is robust to task-irrelevant distractors. We demonstrate our method on a mobile ground robot in open-world exploration scenarios. Given an image of a goal that is up to 80 meters away, our method leverages its representation to explore and discover the goal in under 20 minutes, even amidst previously-unseen obstacles and weather conditions. Please check out the project website for videos of our experiments and information about the real-world dataset used at https://sites.google.com/view/recon-robot.

Offline-to-online RL can make full use of pre-collected offline datasets to initialize policies, resulting in higher sample efficiency and better performance compared to only using online algorithms alone for policy training. However, direct fine-tuning of the pre-trained policy tends to result in sub-optimal performance. A primary reason is that conservative offline RL methods diminish the agent's capability of exploration, thereby impacting online fine-tuning performance. To encourage agent's exploration during online fine-tuning and enhance the overall online fine-tuning performance, we propose a generalized reward augmentation method called Sample Efficient Reward Augmentation (SERA). Specifically, SERA encourages agent to explore by computing Q conditioned entropy as intrinsic reward. The advantage of SERA is that it can extensively utilize offline pre-trained Q to encourage agent uniformly coverage of state space while considering the imbalance between the distributions of high-value and low-value states. Additionally, SERA can be effortlessly plugged into various RL algorithms to improve online fine-tuning and ensure sustained asymptotic improvement. Moreover, extensive experimental results demonstrate that when conducting offline-to-online problems, SERA consistently and effectively enhances the performance of various offline algorithms.

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.

This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while keeping static constraint violation minimal against the optimal constrained linear control policy in hindsight. To establish the results, we introduce an online convex optimization with memory framework under adversarial and static constraints, which serves as a subroutine for the constrained online nonstochastic control algorithms. This subroutine also achieves the state-of-the-art regret and constraint violation bounds for constrained online convex optimization problems, which is of independent interest. Our experiments demonstrate the proposed control algorithms are adaptive to adversarial constraints and achieve smaller cumulative costs and violations. Moreover, our algorithms are less conservative and achieve significantly smaller cumulative costs than the state-of-the-art algorithm.

We introduce Stackelberg Learning from Human Feedback (SLHF), a new framework for preference optimization. SLHF frames the alignment problem as a sequential-move game between two policies: a Leader, which commits to an action, and a Follower, which responds conditionally on the Leader's action. This approach decomposes preference optimization into a refinement problem for the Follower and an optimization problem against an adversary for the Leader. Unlike Reinforcement Learning from Human Feedback (RLHF), which assigns scalar rewards to actions, or Nash Learning from Human Feedback (NLHF), which seeks a simultaneous-move equilibrium, SLHF leverages the asymmetry of sequential play to capture richer preference structures. The sequential design of SLHF naturally enables inference-time refinement, as the Follower learns to improve the Leader's actions, and these refinements can be leveraged through iterative sampling. We compare the solution concepts of SLHF, RLHF, and NLHF, and lay out key advantages in consistency, data sensitivity, and robustness to intransitive preferences. Experiments on large language models demonstrate that SLHF achieves strong alignment across diverse preference datasets, scales from 0.5B to 8B parameters, and yields inference-time refinements that transfer across model families without further fine-tuning.

Flow-based vision-language-action (VLA) models excel in embodied control but suffer from intractable likelihoods during multi-step sampling, hindering online reinforcement learning. We propose \textit{boldsymbolπ-StepNFT} (Step-wise Negative-aware Fine-Tuning), a critic-and-likelihood-free framework that requires only a single forward pass per optimization step and eliminates auxiliary value networks. We identify that wider exploration spaces necessitate finer-grained, step-wise guidance for alignment. Empirically, π-StepNFT unlocks latent potential on LIBERO with competitive few-shot robustness. Moreover, it achieves superior generalization on ManiSkill, outperforming value-based baselines in OOD scenarios by preventing overfitting to multimodal features. This property offers a scalable solution promising for complex real-world applications.

While many real-world problems that might benefit from reinforcement learning, these problems rarely fit into the MDP mold: interacting with the environment is often expensive and specifying reward functions is challenging. Motivated by these challenges, prior work has developed data-driven approaches that learn entirely from samples from the transition dynamics and examples of high-return states. These methods typically learn a reward function from high-return states, use that reward function to label the transitions, and then apply an offline RL algorithm to these transitions. While these methods can achieve good results on many tasks, they can be complex, often requiring regularization and temporal difference updates. In this paper, we propose a method for offline, example-based control that learns an implicit model of multi-step transitions, rather than a reward function. We show that this implicit model can represent the Q-values for the example-based control problem. Across a range of state-based and image-based offline control tasks, our method outperforms baselines that use learned reward functions; additional experiments demonstrate improved robustness and scaling with dataset size.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of mathcal{O}left(Kright), where K is the number of episodes. This is the first result with the optimal K dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of mathcal{O}left(K^{3{4}} right) and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with mathcal{O}left(K^{4{5}}+polyleft(1{lambda_{min}}right) right) regret, for some problem-dependent constant lambda_{min} that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with mathcal{O}left(K^{6{7}} right) regret.

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.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly GRPO, has become the standard for eliciting LLM reasoning. However, its efficiency in exploration and difficulty adaptation remains an open challenge. In this work, we argue that these bottlenecks stem from an implicit advantage symmetry inherent in Group Relative Advantage Estimation (GRAE). This symmetry induces two critical limitations: (i) at the group level, strict symmetry in weights between correct and incorrect trajectories leaves unsampled action logits unchanged, thereby hindering exploration of novel correct solution. (ii) at the sample level, the algorithm implicitly prioritizes medium-difficulty samples, remaining agnostic to the non-stationary demands of difficulty focus. Through controlled experiments, we reveal that this symmetric property is sub-optimal, yielding two pivotal insights: (i) asymmetrically suppressing the advantages of correct trajectories encourages essential exploration. (ii) learning efficiency is maximized by a curriculum-like transition-prioritizing simpler samples initially before gradually shifting to complex ones. Motivated by these findings, we propose Asymmetric GRAE (A-GRAE), which dynamically modulates exploration incentives and sample-difficulty focus. Experiments across seven benchmarks demonstrate that A-GRAE consistently improves GRPO and its variants across both LLMs and MLLMs.

Competitive Pok\'emon Singles (CPS) is a popular strategy game where players learn to exploit their opponent based on imperfect information in battles that can last more than one hundred stochastic turns. AI research in CPS has been led by heuristic tree search and online self-play, but the game may also create a platform to study adaptive policies trained offline on large datasets. We develop a pipeline to reconstruct the first-person perspective of an agent from logs saved from the third-person perspective of a spectator, thereby unlocking a dataset of real human battles spanning more than a decade that grows larger every day. This dataset enables a black-box approach where we train large sequence models to adapt to their opponent based solely on their input trajectory while selecting moves without explicit search of any kind. We study a progression from imitation learning to offline RL and offline fine-tuning on self-play data in the hardcore competitive setting of Pok\'emon's four oldest (and most partially observed) game generations. The resulting agents outperform a recent LLM Agent approach and a strong heuristic search engine. While playing anonymously in online battles against humans, our best agents climb to rankings inside the top 10% of active players.

Direct Preference Optimization (DPO) and its variants have become standard for aligning Large Language Models due to their simplicity and offline stability. However, we identify two fundamental limitations. First, the optimal policy depends on arbitrary modeling choices (scalarization function, reference policy), yielding behavior reflecting parameterization artifacts rather than true preferences. Second, treating response generation in isolation fails to leverage comparative information in pairwise data, leaving the model's capacity for intrinsic self-reflection untapped. To address it, we propose Intrinsic Self-reflective Preference Optimization (InSPO), deriving a globally optimal policy conditioning on both context and alternative responses. We prove this formulation superior to DPO/RLHF while guaranteeing invariance to scalarization and reference choices. InSPO serves as a plug-and-play enhancement without architectural changes or inference overhead. Experiments demonstrate consistent improvements in win rates and length-controlled metrics, validating that unlocking self-reflection yields more robust, human-aligned LLMs. Our Code is available at https://github.com/Skylanding/InSPO.

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL) divergence to constrained target distributions by evolving particles in a dual space defined by a mirror map. Stein Variational Natural Gradient exploits non-Euclidean geometry to more efficiently minimize the KL divergence to unconstrained targets. We derive these samplers from a new class of mirrored Stein operators and adaptive kernels developed in this work. We demonstrate that these new samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods in large-scale unconstrained posterior inference. Finally, we establish the convergence of our new procedures under verifiable conditions on the target distribution.

Learning from human feedback has been shown to improve text-to-image models. These techniques first learn a reward function that captures what humans care about in the task and then improve the models based on the learned reward function. Even though relatively simple approaches (e.g., rejection sampling based on reward scores) have been investigated, fine-tuning text-to-image models with the reward function remains challenging. In this work, we propose using online reinforcement learning (RL) to fine-tune text-to-image models. We focus on diffusion models, defining the fine-tuning task as an RL problem, and updating the pre-trained text-to-image diffusion models using policy gradient to maximize the feedback-trained reward. Our approach, coined DPOK, integrates policy optimization with KL regularization. We conduct an analysis of KL regularization for both RL fine-tuning and supervised fine-tuning. In our experiments, we show that DPOK is generally superior to supervised fine-tuning with respect to both image-text alignment and image quality.

We investigate the effectiveness of reinforcement learning methods for finetuning large language models when transitioning from offline to semi-online to fully online regimes for both verifiable and non-verifiable tasks. Our experiments cover training on verifiable math as well as non-verifiable instruction following with a set of benchmark evaluations for both. Across these settings, we extensively compare online and semi-online Direct Preference Optimization and Group Reward Policy Optimization objectives, and surprisingly find similar performance and convergence between these variants, which all strongly outperform offline methods. We provide a detailed analysis of the training dynamics and hyperparameter selection strategies to achieve optimal results. Finally, we show that multi-tasking with verifiable and non-verifiable rewards jointly yields improved performance across both task types.

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.

Inverse reinforcement learning (IRL) offers a powerful and general framework for learning humans' latent preferences in route recommendation, yet no approach has successfully addressed planetary-scale problems with hundreds of millions of states and demonstration trajectories. In this paper, we introduce scaling techniques based on graph compression, spatial parallelization, and improved initialization conditions inspired by a connection to eigenvector algorithms. We revisit classic IRL methods in the routing context, and make the key observation that there exists a trade-off between the use of cheap, deterministic planners and expensive yet robust stochastic policies. This insight is leveraged in Receding Horizon Inverse Planning (RHIP), a new generalization of classic IRL algorithms that provides fine-grained control over performance trade-offs via its planning horizon. Our contributions culminate in a policy that achieves a 16-24% improvement in route quality at a global scale, and to the best of our knowledge, represents the largest published study of IRL algorithms in a real-world setting to date. We conclude by conducting an ablation study of key components, presenting negative results from alternative eigenvalue solvers, and identifying opportunities to further improve scalability via IRL-specific batching strategies.

The past years have seen Large Language Models (LLMs) strive not only as generative models but also as agents solving textual sequential decision-making tasks. When facing complex environments where their zero-shot abilities are insufficient, recent work showed online Reinforcement Learning (RL) could be used for the LLM agent to discover and learn efficient strategies interactively. However, most prior work sticks to on-policy algorithms, which greatly reduces the scope of methods such agents could use for both exploration and exploitation, such as experience replay and hindsight relabeling. Yet, such methods may be key for LLM learning agents, and in particular when designing autonomous intrinsically motivated agents sampling and pursuing their own goals (i.e. autotelic agents). This paper presents and studies an adaptation of Soft Actor-Critic and hindsight relabeling to LLM agents. Our method not only paves the path towards autotelic LLM agents that learn online but can also outperform on-policy methods in more classic multi-goal RL environments.

Offline reinforcement learning has shown great promise in leveraging large pre-collected datasets for policy learning, allowing agents to forgo often-expensive online data collection. However, to date, offline reinforcement learning from visual observations with continuous action spaces has been relatively under-explored, and there is a lack of understanding of where the remaining challenges lie. In this paper, we seek to establish simple baselines for continuous control in the visual domain. We show that simple modifications to two state-of-the-art vision-based online reinforcement learning algorithms, DreamerV2 and DrQ-v2, suffice to outperform prior work and establish a competitive baseline. We rigorously evaluate these algorithms on both existing offline datasets and a new testbed for offline reinforcement learning from visual observations that better represents the data distributions present in real-world offline RL problems, and open-source our code and data to facilitate progress in this important domain. Finally, we present and analyze several key desiderata unique to offline RL from visual observations, including visual distractions and visually identifiable changes in dynamics.

In view of its power in extracting feature representation, contrastive self-supervised learning has been successfully integrated into the practice of (deep) reinforcement learning (RL), leading to efficient policy learning in various applications. Despite its tremendous empirical successes, the understanding of contrastive learning for RL remains elusive. To narrow such a gap, we study how RL can be empowered by contrastive learning in a class of Markov decision processes (MDPs) and Markov games (MGs) with low-rank transitions. For both models, we propose to extract the correct feature representations of the low-rank model by minimizing a contrastive loss. Moreover, under the online setting, we propose novel upper confidence bound (UCB)-type algorithms that incorporate such a contrastive loss with online RL algorithms for MDPs or MGs. We further theoretically prove that our algorithm recovers the true representations and simultaneously achieves sample efficiency in learning the optimal policy and Nash equilibrium in MDPs and MGs. We also provide empirical studies to demonstrate the efficacy of the UCB-based contrastive learning method for RL. To the best of our knowledge, we provide the first provably efficient online RL algorithm that incorporates contrastive learning for representation learning. Our codes are available at https://github.com/Baichenjia/Contrastive-UCB.

This paper explores the effects of various forms of regularization in the context of language model alignment via self-play. While both reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) require to collect costly human-annotated pairwise preferences, the self-play fine-tuning (SPIN) approach replaces the rejected answers by data generated from the previous iterate. However, the SPIN method presents a performance instability issue in the learning phase, which can be mitigated by playing against a mixture of the two previous iterates. In the same vein, we propose in this work to address this issue from two perspectives: first, by incorporating an additional Kullback-Leibler (KL) regularization to stay at the proximity of the reference policy; second, by using the idea of fictitious play which smoothens the opponent policy across all previous iterations. In particular, we show that the KL-based regularizer boils down to replacing the previous policy by its geometric mixture with the base policy inside of the SPIN loss function. We finally discuss empirical results on MT-Bench as well as on the Hugging Face Open LLM Leaderboard.

Offline reinforcement learning (RL) can in principle synthesize more optimal behavior from a dataset consisting only of suboptimal trials. One way that this can happen is by "stitching" together the best parts of otherwise suboptimal trajectories that overlap on similar states, to create new behaviors where each individual state is in-distribution, but the overall returns are higher. However, in many interesting and complex applications, such as autonomous navigation and dialogue systems, the state is partially observed. Even worse, the state representation is unknown or not easy to define. In such cases, policies and value functions are often conditioned on observation histories instead of states. In these cases, it is not clear if the same kind of "stitching" is feasible at the level of observation histories, since two different trajectories would always have different histories, and thus "similar states" that might lead to effective stitching cannot be leveraged. Theoretically, we show that standard offline RL algorithms conditioned on observation histories suffer from poor sample complexity, in accordance with the above intuition. We then identify sufficient conditions under which offline RL can still be efficient -- intuitively, it needs to learn a compact representation of history comprising only features relevant for action selection. We introduce a bisimulation loss that captures the extent to which this happens, and propose that offline RL can explicitly optimize this loss to aid worst-case sample complexity. Empirically, we show that across a variety of tasks either our proposed loss improves performance, or the value of this loss is already minimized as a consequence of standard offline RL, indicating that it correlates well with good performance.

Existing imitation learning methods mainly focus on making an agent effectively mimic a demonstrated behavior, but do not address the potential contradiction between the behavior style and the objective of a task. There is a general lack of efficient methods that allow an agent to partially imitate a demonstrated behavior to varying degrees, while completing the main objective of a task. In this paper we propose a method called Regularized Soft Actor-Critic which formulates the main task and the imitation task under the Constrained Markov Decision Process framework (CMDP). The main task is defined as the maximum entropy objective used in Soft Actor-Critic (SAC) and the imitation task is defined as a constraint. We evaluate our method on continuous control tasks relevant to video games applications.

Internal modelling of the world -- predicting transitions between previous states X and next states Y under actions Z -- is essential to reasoning and planning for LLMs and VLMs. Learning such models typically requires costly action-labelled trajectories. We propose SWIRL, a self-improvement framework that learns from state-only sequences by treating actions as a latent variable and alternating between Forward World Modelling (FWM) P_θ(Y|X,Z) and an Inverse Dynamics Modelling (IDM) Q_φ(Z|X,Y). SWIRL iterates two phases: (1) Variational Information Maximisation, which updates the FWM to generate next states that maximise conditional mutual information with latent actions given prior states, encouraging identifiable consistency; and (2) ELBO Maximisation, which updates the IDM to explain observed transitions, effectively performing coordinate ascent. Both models are trained with reinforcement learning (specifically, GRPO) with the opposite frozen model's log-probability as a reward signal. We provide theoretical learnability guarantees for both updates, and evaluate SWIRL on LLMs and VLMs across multiple environments: single-turn and multi-turn open-world visual dynamics and synthetic textual environments for physics, web, and tool calling. SWIRL achieves gains of 16% on AURORABench, 28% on ByteMorph, 16% on WorldPredictionBench, and 14% on StableToolBench.

LLM-based Automatic Prompt Optimization, which typically utilizes LLMs as Prompt Optimizers to self-reflect and refine prompts, has shown promising performance in recent studies. Despite the success, the underlying mechanism of this approach remains unexplored, and the true effectiveness of LLMs as Prompt Optimizers requires further validation. In this work, we conducted a comprehensive study to uncover the actual mechanism of LLM-based Prompt Optimization. Our findings reveal that the LLM optimizers struggle to identify the true causes of errors during reflection, tending to be biased by their own prior knowledge rather than genuinely reflecting on the errors. Furthermore, even when the reflection is semantically valid, the LLM optimizers often fail to generate appropriate prompts for the target models with a single prompt refinement step, partly due to the unpredictable behaviors of the target models. Based on the observations, we introduce a new "Automatic Behavior Optimization" paradigm, which directly optimizes the target model's behavior in a more controllable manner. We hope our study can inspire new directions for automatic prompt optimization development.

Progress in many task domains emerges from repeated revisions to previous solution attempts. Training agents that can reliably self-improve over such sequences at inference-time is a natural target for reinforcement learning (RL), yet the naive approach assumes a fixed maximum iteration depth, which can be both costly and arbitrary. We present Exploratory Iteration (ExIt), a family of autocurriculum RL methods that directly exploits the recurrent structure of self-improvement tasks to train LLMs to perform multi-step self-improvement at inference-time while only training on the most informative single-step iterations. ExIt grows a task space by selectively sampling the most informative intermediate, partial histories encountered during an episode for continued iteration, treating these starting points as new self-iteration task instances to train a self-improvement policy. ExIt can further pair with explicit exploration mechanisms to sustain greater task diversity. Across several domains, encompassing competition math, multi-turn tool-use, and machine learning engineering, we demonstrate that ExIt strategies, starting from either a single or many task instances, can produce policies exhibiting strong inference-time self-improvement on held-out task instances, and the ability to iterate towards higher performance over a step budget extending beyond the average iteration depth encountered during training.

We investigate whether self-supervised learning (SSL) can improve online reinforcement learning (RL) from pixels. We extend the contrastive reinforcement learning framework (e.g., CURL) that jointly optimizes SSL and RL losses and conduct an extensive amount of experiments with various self-supervised losses. Our observations suggest that the existing SSL framework for RL fails to bring meaningful improvement over the baselines only taking advantage of image augmentation when the same amount of data and augmentation is used. We further perform evolutionary searches to find the optimal combination of multiple self-supervised losses for RL, but find that even such a loss combination fails to meaningfully outperform the methods that only utilize carefully designed image augmentations. After evaluating these approaches together in multiple different environments including a real-world robot environment, we confirm that no single self-supervised loss or image augmentation method can dominate all environments and that the current framework for joint optimization of SSL and RL is limited. Finally, we conduct the ablation study on multiple factors and demonstrate the properties of representations learned with different approaches.

Reinforcement learning (RL) in the real world necessitates the development of procedures that enable agents to explore without causing harm to themselves or others. The most successful solutions to the problem of safe RL leverage offline data to learn a safe-set, enabling safe online exploration. However, this approach to safe-learning is often constrained by the demonstrations that are available for learning. In this paper we investigate the influence of the quantity and quality of data used to train the initial safe learning problem offline on the ability to learn safe-RL policies online. Specifically, we focus on tasks with spatially extended goal states where we have few or no demonstrations available. Classically this problem is addressed either by using hand-designed controllers to generate data or by collecting user-generated demonstrations. However, these methods are often expensive and do not scale to more complex tasks and environments. To address this limitation we propose an unsupervised RL-based offline data collection procedure, to learn complex and scalable policies without the need for hand-designed controllers or user demonstrations. Our research demonstrates the significance of providing sufficient demonstrations for agents to learn optimal safe-RL policies online, and as a result, we propose optimistic forgetting, a novel online safe-RL approach that is practical for scenarios with limited data. Further, our unsupervised data collection approach highlights the need to balance diversity and optimality for safe online exploration.

In this paper, we introduce the Diff-Instruct* (DI*), an image data-free approach for building one-step text-to-image generative models that align with human preference while maintaining the ability to generate highly realistic images. We frame human preference alignment as online reinforcement learning using human feedback (RLHF), where the goal is to maximize the reward function while regularizing the generator distribution to remain close to a reference diffusion process. Unlike traditional RLHF approaches, which rely on the KL divergence for regularization, we introduce a novel score-based divergence regularization, which leads to significantly better performances. Although the direct calculation of this preference alignment objective remains intractable, we demonstrate that we can efficiently compute its gradient by deriving an equivalent yet tractable loss function. Remarkably, we used Diff-Instruct* to train a Stable Diffusion-XL-based 1-step model, the 2.6B DI*-SDXL-1step text-to-image model, which can generate images of a resolution of 1024x1024 with only 1 generation step. DI*-SDXL-1step model uses only 1.88% inference time and 29.30% GPU memory cost to outperform 12B FLUX-dev-50step significantly in PickScore, ImageReward, and CLIPScore on Parti prompt benchmark and HPSv2.1 on Human Preference Score benchmark, establishing a new state-of-the-art benchmark of human-preferred 1-step text-to-image generative models. Besides the strong quantitative performances, extensive qualitative comparisons also confirm the advantages of DI* in terms of maintaining diversity, improving image layouts, and enhancing aesthetic colors. We have released our industry-ready model on the homepage: https://github.com/pkulwj1994/diff_instruct_star.

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.

Consider learning a policy from example expert behavior, without interaction with the expert or access to reinforcement signal. One approach is to recover the expert's cost function with inverse reinforcement learning, then extract a policy from that cost function with reinforcement learning. This approach is indirect and can be slow. We propose a new general framework for directly extracting a policy from data, as if it were obtained by reinforcement learning following inverse reinforcement learning. We show that a certain instantiation of our framework draws an analogy between imitation learning and generative adversarial networks, from which we derive a model-free imitation learning algorithm that obtains significant performance gains over existing model-free methods in imitating complex behaviors in large, high-dimensional environments.

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.

Offline reinforcement learning (RL) provides a promising solution to learning an agent fully relying on a data-driven paradigm. However, constrained by the limited quality of the offline dataset, its performance is often sub-optimal. Therefore, it is desired to further finetune the agent via extra online interactions before deployment. Unfortunately, offline-to-online RL can be challenging due to two main challenges: constrained exploratory behavior and state-action distribution shift. To this end, we propose a Simple Unified uNcertainty-Guided (SUNG) framework, which naturally unifies the solution to both challenges with the tool of uncertainty. Specifically, SUNG quantifies uncertainty via a VAE-based state-action visitation density estimator. To facilitate efficient exploration, SUNG presents a practical optimistic exploration strategy to select informative actions with both high value and high uncertainty. Moreover, SUNG develops an adaptive exploitation method by applying conservative offline RL objectives to high-uncertainty samples and standard online RL objectives to low-uncertainty samples to smoothly bridge offline and online stages. SUNG achieves state-of-the-art online finetuning performance when combined with different offline RL methods, across various environments and datasets in D4RL benchmark.

The Vision-and-Language Navigation (VLN) task requires an agent to follow natural language instructions and navigate through complex environments. Existing MLLM-based VLN methods primarily rely on imitation learning (IL) and often use DAgger for post-training to mitigate covariate shift. While effective, these approaches incur substantial data collection and training costs. Reinforcement learning (RL) offers a promising alternative. However, prior VLN RL methods lack dynamic interaction with the environment and depend on expert trajectories for reward shaping, rather than engaging in open-ended active exploration. This restricts the agent's ability to discover diverse and plausible navigation routes. To address these limitations, we propose ActiveVLN, a VLN framework that explicitly enables active exploration through multi-turn RL. In the first stage, a small fraction of expert trajectories is used for IL to bootstrap the agent. In the second stage, the agent iteratively predicts and executes actions, automatically collects diverse trajectories, and optimizes multiple rollouts via the GRPO objective. To further improve RL efficiency, we introduce a dynamic early-stopping strategy to prune long-tail or likely failed trajectories, along with additional engineering optimizations. Experiments show that ActiveVLN achieves the largest performance gains over IL baselines compared to both DAgger-based and prior RL-based post-training methods, while reaching competitive performance with state-of-the-art approaches despite using a smaller model. Code and data will be released soon.

Although reinforcement learning methods offer a powerful framework for automatic skill acquisition, for practical learning-based control problems in domains such as robotics, imitation learning often provides a more convenient and accessible alternative. In particular, an interactive imitation learning method such as DAgger, which queries a near-optimal expert to intervene online to collect correction data for addressing the distributional shift challenges that afflict na\"ive behavioral cloning, can enjoy good performance both in theory and practice without requiring manually specified reward functions and other components of full reinforcement learning methods. In this paper, we explore how off-policy reinforcement learning can enable improved performance under assumptions that are similar but potentially even more practical than those of interactive imitation learning. Our proposed method uses reinforcement learning with user intervention signals themselves as rewards. This relaxes the assumption that intervening experts in interactive imitation learning should be near-optimal and enables the algorithm to learn behaviors that improve over the potential suboptimal human expert. We also provide a unified framework to analyze our RL method and DAgger; for which we present the asymptotic analysis of the suboptimal gap for both methods as well as the non-asymptotic sample complexity bound of our method. We then evaluate our method on challenging high-dimensional continuous control simulation benchmarks as well as real-world robotic vision-based manipulation tasks. The results show that it strongly outperforms DAgger-like approaches across the different tasks, especially when the intervening experts are suboptimal. Code and videos can be found on the project website: rlif-page.github.io

Off-policy reinforcement learning (RL) for large language models (LLMs) is attracting growing interest, driven by practical constraints in real-world applications, the complexity of LLM-RL infrastructure, and the need for further innovations of RL methodologies. While classic REINFORCE and its modern variants like Group Relative Policy Optimization (GRPO) are typically regarded as on-policy algorithms with limited tolerance of off-policyness, we present in this work a first-principles derivation for group-relative REINFORCE without assuming a specific training data distribution, showing that it admits a native off-policy interpretation. This perspective yields two general principles for adapting REINFORCE to off-policy settings: regularizing policy updates, and actively shaping the data distribution. Our analysis demystifies some myths about the roles of importance sampling and clipping in GRPO, unifies and reinterprets two recent algorithms -- Online Policy Mirror Descent (OPMD) and Asymmetric REINFORCE (AsymRE) -- as regularized forms of the REINFORCE loss, and offers theoretical justification for seemingly heuristic data-weighting strategies. Our findings lead to actionable insights that are validated with extensive empirical studies, and open up new opportunities for principled algorithm design in off-policy RL for LLMs. Source code for this work is available at https://github.com/modelscope/Trinity-RFT/tree/main/examples/rec_gsm8k.

We initiate the study of Multi-Agent Reinforcement Learning from Human Feedback (MARLHF), exploring both theoretical foundations and empirical validations. We define the task as identifying Nash equilibrium from a preference-only offline dataset in general-sum games, a problem marked by the challenge of sparse feedback signals. Our theory establishes the upper complexity bounds for Nash Equilibrium in effective MARLHF, demonstrating that single-policy coverage is inadequate and highlighting the importance of unilateral dataset coverage. These theoretical insights are verified through comprehensive experiments. To enhance the practical performance, we further introduce two algorithmic techniques. (1) We propose a Mean Squared Error (MSE) regularization along the time axis to achieve a more uniform reward distribution and improve reward learning outcomes. (2) We utilize imitation learning to approximate the reference policy, ensuring stability and effectiveness in training. Our findings underscore the multifaceted approach required for MARLHF, paving the way for effective preference-based multi-agent systems.

In machine learning for sequential decision-making, an algorithmic agent learns to interact with an environment while receiving feedback in the form of a reward signal. However, in many unstructured real-world settings, such a reward signal is unknown and humans cannot reliably craft a reward signal that correctly captures desired behavior. To solve tasks in such unstructured and open-ended environments, we present Demonstration-Inferred Preference Reinforcement Learning (DIP-RL), an algorithm that leverages human demonstrations in three distinct ways, including training an autoencoder, seeding reinforcement learning (RL) training batches with demonstration data, and inferring preferences over behaviors to learn a reward function to guide RL. We evaluate DIP-RL in a tree-chopping task in Minecraft. Results suggest that the method can guide an RL agent to learn a reward function that reflects human preferences and that DIP-RL performs competitively relative to baselines. DIP-RL is inspired by our previous work on combining demonstrations and pairwise preferences in Minecraft, which was awarded a research prize at the 2022 NeurIPS MineRL BASALT competition, Learning from Human Feedback in Minecraft. Example trajectory rollouts of DIP-RL and baselines are located at https://sites.google.com/view/dip-rl.

World models simulate dynamic environments, enabling agents to interact with diverse input modalities. Although recent advances have improved the visual quality and temporal consistency of video world models, their ability of accurately modeling human-specified actions remains under-explored. Reinforcement learning presents a promising approach for directly improving the suboptimal action-following capability of pre-trained models, assuming that an appropriate reward function can be defined. However, transferring reinforcement learning post-training methods to world model is impractical due to the prohibitive cost of large-scale preference annotations and the infeasibility of constructing rule-based video verifiers. To address this gap, we propose Reinforcement Learning with Inverse Rewards (RLIR), a post-training framework that derives verifiable reward signals by recovering input actions from generated videos using an Inverse Dynamics Model. By mapping high-dimensional video modality to a low-dimensional action space, RLIR provides an objective and verifiable reward for optimization via Group Relative Policy Optimization. Experiments across autoregressive and diffusion paradigms demonstrate 5-10% gains in action-following, up to 10% improvements in visual quality, and higher human preference scores, establishing RLIR as the first post-training method specifically designed to enhance action-following in video world models.

Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates continual learning (CL) to update models online, enabling adaptation to new tasks while preserving past knowledge to prevent catastrophic forgetting. Nowadays, with the flourish of large pre-trained models (LPMs), efficiency has become increasingly critical for CL, due to their substantial computational demands and growing parameter sizes. In this paper, we introduce TreeLoRA (K-D Tree of Low-Rank Adapters), a novel approach that constructs layer-wise adapters by leveraging hierarchical gradient similarity to enable efficient CL, particularly for LPMs. To reduce the computational burden of task similarity estimation, we employ bandit techniques to develop an algorithm based on lower confidence bounds to efficiently explore the task structure. Furthermore, we use sparse gradient updates to facilitate parameter optimization, making the approach better suited for LPMs. Theoretical analysis is provided to justify the rationale behind our approach, and experiments on both vision transformers (ViTs) and large language models (LLMs) demonstrate the effectiveness and efficiency of our approach across various domains, including vision and natural language processing tasks.

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.

Preference optimization, particularly through Reinforcement Learning from Human Feedback (RLHF), has achieved significant success in aligning Large Language Models (LLMs) to adhere to human intentions. Unlike offline alignment with a fixed dataset, online feedback collection from humans or AI on model generations typically leads to more capable reward models and better-aligned LLMs through an iterative process. However, achieving a globally accurate reward model requires systematic exploration to generate diverse responses that span the vast space of natural language. Random sampling from standard reward-maximizing LLMs alone is insufficient to fulfill this requirement. To address this issue, we propose a bilevel objective optimistically biased towards potentially high-reward responses to actively explore out-of-distribution regions. By solving the inner-level problem with the reparameterized reward function, the resulting algorithm, named Self-Exploring Language Models (SELM), eliminates the need for a separate RM and iteratively updates the LLM with a straightforward objective. Compared to Direct Preference Optimization (DPO), the SELM objective reduces indiscriminate favor of unseen extrapolations and enhances exploration efficiency. Our experimental results demonstrate that when finetuned on Zephyr-7B-SFT and Llama-3-8B-Instruct models, SELM significantly boosts the performance on instruction-following benchmarks such as MT-Bench and AlpacaEval 2.0, as well as various standard academic benchmarks in different settings. Our code and models are available at https://github.com/shenao-zhang/SELM.

Typical post-training paradigms for Large Vision-and-Language Models (LVLMs) include Supervised Fine-Tuning (SFT) and Reinforcement Learning with Verifiable Rewards (RLVR). SFT leverages external guidance to inject new knowledge, whereas RLVR utilizes internal reinforcement to enhance reasoning capabilities and overall performance. However, our analysis reveals that SFT often leads to sub-optimal performance, while RLVR struggles with tasks that exceed the model's internal knowledge base. To address these limitations, we propose ViSurf (Visual Supervised-and-Reinforcement Fine-Tuning), a unified post-training paradigm that integrates the strengths of both SFT and RLVR within a single stage. We analyze the derivation of the SFT and RLVR objectives to establish the ViSurf objective, providing a unified perspective on these two paradigms. The core of ViSurf involves injecting ground-truth labels into the RLVR rollouts, thereby providing simultaneous external supervision and internal reinforcement. Furthermore, we introduce three novel reward control strategies to stabilize and optimize the training process. Extensive experiments across several diverse benchmarks demonstrate the effectiveness of ViSurf, outperforming both individual SFT, RLVR, and two-stage SFT \textrightarrow RLVR. In-depth analysis corroborates these findings, validating the derivation and design principles of ViSurf.

Sample efficiency and exploration remain critical challenges in Deep Reinforcement Learning (DRL), particularly in complex domains. Offline RL, which enables agents to learn optimal policies from static, pre-collected datasets, has emerged as a promising alternative. However, offline RL is constrained by issues such as out-of-distribution (OOD) actions that limit policy performance and generalization. To overcome these limitations, we propose Meta Offline-Online Reinforcement Learning (MOORL), a hybrid framework that unifies offline and online RL for efficient and scalable learning. While previous hybrid methods rely on extensive design components and added computational complexity to utilize offline data effectively, MOORL introduces a meta-policy that seamlessly adapts across offline and online trajectories. This enables the agent to leverage offline data for robust initialization while utilizing online interactions to drive efficient exploration. Our theoretical analysis demonstrates that the hybrid approach enhances exploration by effectively combining the complementary strengths of offline and online data. Furthermore, we demonstrate that MOORL learns a stable Q-function without added complexity. Extensive experiments on 28 tasks from the D4RL and V-D4RL benchmarks validate its effectiveness, showing consistent improvements over state-of-the-art offline and hybrid RL baselines. With minimal computational overhead, MOORL achieves strong performance, underscoring its potential for practical applications in real-world scenarios.

We present DuPO, a dual learning-based preference optimization framework that generates annotation-free feedback via a generalized duality. DuPO addresses two key limitations: Reinforcement Learning with Verifiable Rewards (RLVR)'s reliance on costly labels and applicability restricted to verifiable tasks, and traditional dual learning's restriction to strictly dual task pairs (e.g., translation and back-translation). Specifically, DuPO decomposes a primal task's input into known and unknown components, then constructs its dual task to reconstruct the unknown part using the primal output and known information (e.g., reversing math solutions to recover hidden variables), broadening applicability to non-invertible tasks. The quality of this reconstruction serves as a self-supervised reward to optimize the primal task, synergizing with LLMs' ability to instantiate both tasks via a single model. Empirically, DuPO achieves substantial gains across diverse tasks: it enhances the average translation quality by 2.13 COMET over 756 directions, boosts the mathematical reasoning accuracy by an average of 6.4 points on three challenge benchmarks, and enhances performance by 9.3 points as an inference-time reranker (trading computation for accuracy). These results position DuPO as a scalable, general, and annotation-free paradigm for LLM optimization.

Our aim is to build autonomous agents that can solve tasks in environments like Minecraft. To do so, we used an imitation learning-based approach. We formulate our control problem as a search problem over a dataset of experts' demonstrations, where the agent copies actions from a similar demonstration trajectory of image-action pairs. We perform a proximity search over the BASALT MineRL-dataset in the latent representation of a Video PreTraining model. The agent copies the actions from the expert trajectory as long as the distance between the state representations of the agent and the selected expert trajectory from the dataset do not diverge. Then the proximity search is repeated. Our approach can effectively recover meaningful demonstration trajectories and show human-like behavior of an agent in the Minecraft environment.

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

Balancing exploration and exploitation remains a central challenge in reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs). Current RLVR methods often overemphasize exploitation, leading to entropy collapse, diminished exploratory capacity, and ultimately limited performance gains. Although techniques that increase policy stochasticity can promote exploration, they frequently fail to escape dominant behavioral modes. This creates a self-reinforcing loop-repeatedly sampling and rewarding dominant modes-that further erodes exploration. We introduce Exploration-Enhanced Policy Optimization (EEPO), a framework that promotes exploration via two-stage rollouts with adaptive unlearning. In the first stage, the model generates half of the trajectories; it then undergoes a lightweight unlearning step to temporarily suppress these sampled responses, forcing the second stage to explore different regions of the output space. This sample-then-forget mechanism disrupts the self-reinforcing loop and promotes wider exploration during rollouts. Across five reasoning benchmarks, EEPO outperforms GRPO, achieving average relative gains of 24.3% on Qwen2.5-3B, 33.0% on Llama3.2-3B-Instruct, and 10.4% on Qwen3-8B-Base.

End-to-End (E2E) solutions have emerged as a mainstream approach for autonomous driving systems, with Vision-Language-Action (VLA) models representing a new paradigm that leverages pre-trained multimodal knowledge from Vision-Language Models (VLMs) to interpret and interact with complex real-world environments. However, these methods remain constrained by the limitations of imitation learning, which struggles to inherently encode physical rules during training. Existing approaches often rely on complex rule-based post-refinement, employ reinforcement learning that remains largely limited to simulation, or utilize diffusion guidance that requires computationally expensive gradient calculations. To address these challenges, we introduce ReflectDrive, a novel learning-based framework that integrates a reflection mechanism for safe trajectory generation via discrete diffusion. We first discretize the two-dimensional driving space to construct an action codebook, enabling the use of pre-trained Diffusion Language Models for planning tasks through fine-tuning. Central to our approach is a safety-aware reflection mechanism that performs iterative self-correction without gradient computation. Our method begins with goal-conditioned trajectory generation to model multi-modal driving behaviors. Based on this, we apply local search methods to identify unsafe tokens and determine feasible solutions, which then serve as safe anchors for inpainting-based regeneration. Evaluated on the NAVSIM benchmark, ReflectDrive demonstrates significant advantages in safety-critical trajectory generation, offering a scalable and reliable solution for autonomous driving systems.

Rewards remain an uninterpretable way to specify tasks for Reinforcement Learning, as humans are often unable to predict the optimal behavior of any given reward function, leading to poor reward design and reward hacking. Language presents an appealing way to communicate intent to agents and bypass reward design, but prior efforts to do so have been limited by costly and unscalable labeling efforts. In this work, we propose a method for a completely unsupervised alternative to grounding language instructions in a zero-shot manner to obtain policies. We present a solution that takes the form of imagine, project, and imitate: The agent imagines the observation sequence corresponding to the language description of a task, projects the imagined sequence to our target domain, and grounds it to a policy. Video-language models allow us to imagine task descriptions that leverage knowledge of tasks learned from internet-scale video-text mappings. The challenge remains to ground these generations to a policy. In this work, we show that we can achieve a zero-shot language-to-behavior policy by first grounding the imagined sequences in real observations of an unsupervised RL agent and using a closed-form solution to imitation learning that allows the RL agent to mimic the grounded observations. Our method, RLZero, is the first to our knowledge to show zero-shot language to behavior generation abilities without any supervision on a variety of tasks on simulated domains. We further show that RLZero can also generate policies zero-shot from cross-embodied videos such as those scraped from YouTube.

Intelligent agents progress by continually refining their capabilities through actively exploring environments. Yet robot policies often lack sufficient exploration capability due to action mode collapse. Existing methods that encourage exploration typically rely on random perturbations, which are unsafe and induce unstable, erratic behaviors, thereby limiting their effectiveness. We propose Self-Improvement via On-Manifold Exploration (SOE), a framework that enhances policy exploration and improvement in robotic manipulation. SOE learns a compact latent representation of task-relevant factors and constrains exploration to the manifold of valid actions, ensuring safety, diversity, and effectiveness. It can be seamlessly integrated with arbitrary policy models as a plug-in module, augmenting exploration without degrading the base policy performance. Moreover, the structured latent space enables human-guided exploration, further improving efficiency and controllability. Extensive experiments in both simulation and real-world tasks demonstrate that SOE consistently outperforms prior methods, achieving higher task success rates, smoother and safer exploration, and superior sample efficiency. These results establish on-manifold exploration as a principled approach to sample-efficient policy self-improvement. Project website: https://ericjin2002.github.io/SOE

In large-scale AI training, Sparse Mixture-of-Experts (s-MoE) layers enable scaling by activating only a small subset of experts per token. An operational challenge in this design is load balancing: routing tokens to minimize the number of idle experts, which is important for the efficient utilization of (costly) GPUs. We provide a theoretical framework for analyzing the Auxiliary-Loss-Free Load Balancing (ALF-LB) procedure -- proposed by DeepSeek's Wang et al. (2024) -- by casting it as a one-step-per-iteration primal-dual method for an assignment problem. First, in a stylized deterministic setting, our framework yields several insightful structural properties: (i) a monotonic improvement of a Lagrangian objective, (ii) a preference rule that moves tokens from overloaded to underloaded experts, and (iii) an approximate-balancing guarantee. Then, we incorporate the stochastic and dynamic nature of AI training using a generalized online optimization formulation. In the online setting, we derive a strong convexity property of the objective that leads to a logarithmic expected regret bound under certain step-size choices. Additionally, we present real experiments on 1B-parameter DeepSeekMoE models to complement our theoretical findings. Together, these results build a principled framework for analyzing the Auxiliary-Loss-Free Load Balancing of s-MoE in AI models.

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a rater or preference model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

We present the workflow of Online Iterative Reinforcement Learning from Human Feedback (RLHF) in this technical report, which is widely reported to outperform its offline counterpart by a large margin in the recent large language model (LLM) literature. However, existing open-source RLHF projects are still largely confined to the offline learning setting. In this technical report, we aim to fill in this gap and provide a detailed recipe that is easy to reproduce for online iterative RLHF. In particular, since online human feedback is usually infeasible for open-source communities with limited resources, we start by constructing preference models using a diverse set of open-source datasets and use the constructed proxy preference model to approximate human feedback. Then, we discuss the theoretical insights and algorithmic principles behind online iterative RLHF, followed by a detailed practical implementation. Our trained LLM, SFR-Iterative-DPO-LLaMA-3-8B-R, achieves impressive performance on LLM chatbot benchmarks, including AlpacaEval-2, Arena-Hard, and MT-Bench, as well as other academic benchmarks such as HumanEval and TruthfulQA. We have shown that supervised fine-tuning (SFT) and iterative RLHF can obtain state-of-the-art performance with fully open-source datasets. Further, we have made our models, curated datasets, and comprehensive step-by-step code guidebooks publicly available. Please refer to https://github.com/RLHFlow/RLHF-Reward-Modeling and https://github.com/RLHFlow/Online-RLHF for more detailed information.

Imitation from observation is a computational technique that teaches an agent on how to mimic the behavior of an expert by observing only the sequence of states from the expert demonstrations. Recent approaches learn the inverse dynamics of the environment and an imitation policy by interleaving epochs of both models while changing the demonstration data. However, such approaches often get stuck into sub-optimal solutions that are distant from the expert, limiting their imitation effectiveness. We address this problem with a novel approach that overcomes the problem of reaching bad local minima by exploring: (I) a self-attention mechanism that better captures global features of the states; and (ii) a sampling strategy that regulates the observations that are used for learning. We show empirically that our approach outperforms the state-of-the-art approaches in four different environments by a large margin.

Search agents have achieved significant advancements in enabling intelligent information retrieval and decision-making within interactive environments. Although reinforcement learning has been employed to train agentic models capable of more dynamic interactive retrieval, existing methods are limited by shallow tool-use depth and the accumulation of errors over multiple iterative interactions. In this paper, we present WebSeer, a more intelligent search agent trained via reinforcement learning enhanced with a self-reflection mechanism. Specifically, we construct a large dataset annotated with reflection patterns and design a two-stage training framework that unifies cold start and reinforcement learning within the self-reflection paradigm for real-world web-based environments, which enables the model to generate longer and more reflective tool-use trajectories. Our approach substantially extends tool-use chains and improves answer accuracy. Using a single 14B model, we achieve state-of-the-art results on HotpotQA and SimpleQA, with accuracies of 72.3% and 90.0%, respectively, and demonstrate strong generalization to out-of-distribution datasets. The code is available at https://github.com/99hgz/WebSeer

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves mathcal{O}(epsilon^{-3}) and mathcal{O}(epsilon^{-2}) sample complexities for epsilon-first-order stationarity and epsilon-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a mathcal{O}(epsilon^{-4}) sample complexity for a simple policy gradient method with a linear regression subroutine.

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 study methods for efficiently aligning large language models (LLMs) with human preferences given budgeted online feedback. We first formulate the LLM alignment problem in the frame of contextual dueling bandits. This formulation, subsuming recent paradigms such as online RLHF and online DPO, inherently quests for sample-efficient algorithms that incorporate online active exploration. Leveraging insights from bandit theory, we introduce a unified algorithm based on Thompson sampling and highlight its applications in two distinct LLM alignment scenarios. The practical agent that efficiently implements this algorithm, named SEA (Sample-Efficient Alignment), is empirically validated through extensive experiments across three model scales (1B, 2.8B, 6.9B) and three preference learning algorithms (DPO, IPO, SLiC). The results demonstrate that SEA achieves highly sample-efficient alignment with oracle's preferences, outperforming recent active exploration methods for LLMs. Additionally, we release the implementation of SEA together with an efficient codebase designed for online alignment of LLMs, aiming to accelerate future research in this field.

Training practical agents usually involve offline and online reinforcement learning (RL) to balance the policy's performance and interaction costs. In particular, online fine-tuning has become a commonly used method to correct the erroneous estimates of out-of-distribution data learned in the offline training phase. However, even limited online interactions can be inaccessible or catastrophic for high-stake scenarios like healthcare and autonomous driving. In this work, we introduce an interaction-free training scheme dubbed Offline-with-Action-Preferences (OAP). The main insight is that, compared to online fine-tuning, querying the preferences between pre-collected and learned actions can be equally or even more helpful to the erroneous estimate problem. By adaptively encouraging or suppressing policy constraint according to action preferences, OAP could distinguish overestimation from beneficial policy improvement and thus attains a more accurate evaluation of unseen data. Theoretically, we prove a lower bound of the behavior policy's performance improvement brought by OAP. Moreover, comprehensive experiments on the D4RL benchmark and state-of-the-art algorithms demonstrate that OAP yields higher (29% on average) scores, especially on challenging AntMaze tasks (98% higher).

Reinforcement learning drives recent advances in LLM reasoning and agentic capabilities, yet current approaches struggle with both exploration and exploitation. Exploration suffers from low success rates on difficult tasks and high costs of repeated rollouts from scratch. Exploitation suffers from coarse credit assignment and training instability: Trajectory-level rewards penalize valid prefixes for later errors, and failure-dominated groups overwhelm the few positive signals, leaving optimization without constructive direction. To this end, we propose R^3L, Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification. To synthesize high-quality trajectories, R^3L shifts from stochastic sampling to active synthesis via reflect-then-retry, leveraging language feedback to diagnose errors, transform failed attempts into successful ones, and reduce rollout costs by restarting from identified failure points. With errors diagnosed and localized, Pivotal Credit Assignment updates only the diverging suffix where contrastive signals exist, excluding the shared prefix from gradient update. Since failures dominate on difficult tasks and reflect-then-retry produces off-policy data, risking training instability, Positive Amplification upweights successful trajectories to ensure positive signals guide the optimization process. Experiments on agentic and reasoning tasks demonstrate 5\% to 52\% relative improvements over baselines while maintaining training stability. Our code is released at https://github.com/shiweijiezero/R3L.

Both online and offline RLHF methods such as PPO and DPO have been extremely successful in aligning AI with human preferences. Despite their success, the existing methods suffer from a fundamental problem that their optimal solution is highly task-dependent (i.e., not robust to out-of-distribution (OOD) tasks). Here we address this challenge by proposing Self-Improving Robust Preference Optimization SRPO, a practical and mathematically principled offline RLHF framework that is completely robust to the changes in the task. The key idea of SRPO is to cast the problem of learning from human preferences as a self-improvement process, which can be mathematically expressed in terms of a min-max objective that aims at joint optimization of self-improvement policy and the generative policy in an adversarial fashion. The solution for this optimization problem is independent of the training task and thus it is robust to its changes. We then show that this objective can be re-expressed in the form of a non-adversarial offline loss which can be optimized using standard supervised optimization techniques at scale without any need for reward model and online inference. We show the effectiveness of SRPO in terms of AI Win-Rate (WR) against human (GOLD) completions. In particular, when SRPO is evaluated on the OOD XSUM dataset, it outperforms the celebrated DPO by a clear margin of 15% after 5 self-revisions, achieving WR of 90%.

This work presents In-Context Policy Iteration, an algorithm for performing Reinforcement Learning (RL), in-context, using foundation models. While the application of foundation models to RL has received considerable attention, most approaches rely on either (1) the curation of expert demonstrations (either through manual design or task-specific pretraining) or (2) adaptation to the task of interest using gradient methods (either fine-tuning or training of adapter layers). Both of these techniques have drawbacks. Collecting demonstrations is labor-intensive, and algorithms that rely on them do not outperform the experts from which the demonstrations were derived. All gradient techniques are inherently slow, sacrificing the "few-shot" quality that made in-context learning attractive to begin with. In this work, we present an algorithm, ICPI, that learns to perform RL tasks without expert demonstrations or gradients. Instead we present a policy-iteration method in which the prompt content is the entire locus of learning. ICPI iteratively updates the contents of the prompt from which it derives its policy through trial-and-error interaction with an RL environment. In order to eliminate the role of in-weights learning (on which approaches like Decision Transformer rely heavily), we demonstrate our algorithm using Codex, a language model with no prior knowledge of the domains on which we evaluate it.

Large language models excel with reinforcement learning (RL), but fully unlocking this potential requires a mid-training stage. An effective mid-training phase should identify a compact set of useful actions and enable fast selection among them through online RL. We formalize this intuition by presenting the first theoretical result on how mid-training shapes post-training: it characterizes an action subspace that minimizes both the value approximation error from pruning and the RL error during subsequent planning. Our analysis reveals two key determinants of mid-training effectiveness: pruning efficiency, which shapes the prior of the initial RL policy, and its impact on RL convergence, which governs the extent to which that policy can be improved via online interactions. These results suggest that mid-training is most effective when the decision space is compact and the effective horizon is short, highlighting the importance of operating in the space of action abstractions rather than primitive actions. Building on these insights, we propose Reasoning as Action Abstractions (RA3), a scalable mid-training algorithm. Specifically, we derive a sequential variational lower bound and optimize it by iteratively discovering temporally-consistent latent structures via RL, followed by fine-tuning on the bootstrapped data. Experiments on code generation tasks demonstrate the effectiveness of our approach. Across multiple base models, RA3 improves the average performance on HumanEval and MBPP by 8 and 4 points over the base model and the next-token prediction baseline. Furthermore, RA3 achieves faster convergence and higher asymptotic performance in RLVR on HumanEval+, MBPP+, LiveCodeBench, and Codeforces.

Aligning text-to-image (T2I) diffusion models with human preferences has emerged as a critical research challenge. While recent advances in this area have extended preference optimization techniques from large language models (LLMs) to the diffusion setting, they often struggle with limited exploration. In this work, we propose a novel and orthogonal approach to enhancing diffusion-based preference optimization. First, we introduce a stable reference model update strategy that relaxes the frozen reference model, encouraging exploration while maintaining a stable optimization anchor through reference model regularization. Second, we present a timestep-aware training strategy that mitigates the reward scale imbalance problem across timesteps. Our method can be integrated into various preference optimization algorithms. Experimental results show that our approach improves the performance of state-of-the-art methods on human preference evaluation benchmarks.

A prevailing view in Reinforcement Learning for Verifiable Rewards (RLVR) interprets recent progress through the lens of an exploration-exploitation trade-off, a perspective largely shaped by token-level metrics. We re-examine this perspective, proposing that this perceived trade-off may not be a fundamental constraint but rather an artifact of the measurement level. To investigate this, we shift the analysis to the semantically rich hidden-state space, adopting Effective Rank (ER) to quantify exploration and proposing its novel first- and second-order derivatives, named Effective Rank Velocity (ERV) and Effective Rank Acceleration (ERA), to capture exploitation dynamics. Our analysis reveals that at the hidden-state level, exploration and exploitation could be decoupled (Sec. 4). This finding reveals an opportunity to enhance both capacities simultaneously. This insight motivates our method, Velocity-Exploiting Rank-Learning (VERL), the first to operationalize the principle of synergistic exploration-exploitation enhancement by directly shaping the RL advantage function. The key innovation is leveraging the theoretically stable ERA as a predictive meta-controller to create a synergistic, dual-channel incentive structure. Instead of forcing a trade-off, VERL prospectively amplifies rewards for exploration to preempt overconfidence and reinforces exploitative gains to consolidate reasoning. Experiments across diverse LLMs and reasoning benchmarks show consistent gains, including up to 21.4% absolute accuracy improvement on the challenging Gaokao 2024 dataset.

Large Language Models (LLMs) have a natural role in answering complex queries about data streams, but the high computational cost of LLM inference makes them infeasible in many such tasks. We propose online cascade learning, the first approach to address this challenge. The objective here is to learn a "cascade" of models, starting with lower-capacity models (such as logistic regression) and ending with a powerful LLM, along with a deferral policy that determines the model to be used on a given input. We formulate the task of learning cascades online as an imitation-learning problem, where smaller models are updated over time imitating the collected LLM demonstrations, and give a no-regret algorithm for the problem. Experimental results across four benchmarks show that our method parallels LLMs in accuracy while cutting down inference costs by as much as 90% with strong robustness against input distribution shifts, underscoring its efficacy and adaptability in stream processing.