Daily Papers

On-Policy Self-Distillation (OPSD) has emerged as a popular paradigm for large language model (LLM) self-improvement, allowing models to act as their own teachers by leveraging privileged information such as ground-truth solutions. However, recent findings indicate that OPSD can severely degrade the performance of LLMs on complex reasoning tasks: By forcing the student to imitate an artificially confident reasoning trace conditioned on privileged information, OPSD inadvertently suppresses expressions of uncertainty and penalizes the exploratory, self-corrective behaviors required to solve challenging problems. To address this, we introduce Negative Self-Distillation (NSD), a new framework that optimizes LLMs by diverging from flawed reasoning rather than imitating privileged solutions. Instead of relying on ground-truth answers or external supervision, NSD uses the model itself to generate a question-specific negative condition (eg, acting as a ``careless reasoner'') and pushes the student's distribution away from this self-generated negative teacher. Naively applying unlearning objectives to achieve this divergence is problematic, as flawed reasoning tokens are confounded with basic linguistic tokens; indiscriminately penalizing both risks catastrophically degrading the model's foundational language capabilities. We resolve this by designing a dynamic gating mechanism that automatically identifies and isolates reasoning-critical tokens, ensuring gradient updates target only behavioral flaws while preserving the model's linguistic priors. Empirically, NSD consistently outperforms OPSD and other label-free, self-bootstrapping reinforcement learning (RL) baselines.

The limited capacity for fine-grained visual perception presents a critical bottleneck for Vision-Language Models (VLMs) in real-world applications. Addressing this is challenging due to the scarcity of high-quality data and the limitations of existing methods: supervised fine-tuning (SFT) often compromises general capabilities, while reinforcement fine-tuning (RFT) prioritizes textual reasoning over visual perception. To bridge this gap, we propose a novel two-stage task that structures visual perception learning as a coarse-to-fine progressive process. Based on this task formulation, we develop ViPER, a self-bootstrapping framework specifically designed to enable iterative evolution through self-critiquing and self-prediction. By synergistically integrating image-level and instance-level reconstruction with a two-stage reinforcement learning strategy, ViPER establishes a closed-loop training paradigm, where internally synthesized data directly fuel the enhancement of perceptual ability. Applied to the Qwen2.5-VL family, ViPER produces the Qwen-Viper series. With an average gain of 1.7% on seven comprehensive benchmarks spanning various tasks and up to 6.0% on fine-grained perception, Qwen-Viper consistently demonstrates superior performance across different vision-language scenarios while maintaining generalizability. Beyond enabling self-improvement in perceptual capabilities, ViPER provides concrete evidence for the reciprocal relationship between generation and understanding, a breakthrough to developing more autonomous and capable VLMs.

Modern large language models (LLMs) can translate natural-language descriptions into operations research (OR) formulations. Post-training techniques including reinforcement learning and on-policy self-distillation have further improved this capability. However, three limitations remain in training LLMs for OR formulations. First, training commonly relies on synthetic formulations validated by human experts or stronger models, constraining scalable supervision. Second, credit assignment is either coarse or costly: outcome rewards score an entire trajectory without locating the responsible modeling decision, whereas process-level supervision requires an additional evaluator. Third, privileged self-distillation can induce style mismatch by using solver context unavailable at deployment. We find that a model can improve from solver-artifact feedback generated by its own rollouts, making self-distillation a practical, evaluator-free source of dense supervision. Therefore, we propose SOLID: Solver-Informed On-Policy LearnIng through Self-Distillation, a novel framework for self-improving OR language models without verified answers or external evaluators. SOLID executes candidate programs from multiple rollouts, clusters their objectives, and selects a majority-group artifact as a pseudo-reference. The model then performs updates using group-relative advantages and dense self-supervision signals. Across multiple OR benchmarks, SOLID improves solution accuracy for both general-purpose and OR-tuned models over outcome-only group-relative training. These results show that solver artifacts can support scalable self-improvement without trusted answers.

We introduce Self-Verified Reasoner (SVR-R1), a multi-turn RL framework that turns a model's own verification into a learning signal for multimodal reasoning. For each query, the model proposes an answer using the same weights, and issues a binary self-verdict (Yes/No). A 'No' triggers a second-chance rethink; a 'Yes,' or a turn cap, finalizes the output for computing the outcome-based reward. SVR-R1 is implemented with GRPO and an asynchronous multi-turn rollout framework and needs no external supervision or auxiliary critics. We evaluate SVR-R1 on vision-language reasoning benchmarks and show that it improves accuracy by a large margin over strong standard GRPO baselines. Training dynamics show decreasing reliance on verification-fewer verification turns, yet higher test accuracy-indicating that the gap between verification and generation narrows as the policy internalizes self-correction and chooses the most confident answer via our framework. SVR-R1 bridges the less explored intersection of inference-time self-refinement and RL training for VLMs, offering a simple yet effective recipe for bootstrapping multimodal reasoning. We will open-source SVR-R1 to facilitate future research in VLMs.

Long context reasoning in large language models (LLMs) has demonstrated enhancement of their cognitive capabilities via chain-of-thought (CoT) inference. Training such models is usually done via reinforcement learning with verifiable rewards (RLVR) in reasoning based problems, like math and programming. However, RLVR is limited by several bottlenecks, such as, lack of dense reward, and inadequate sample efficiency. As a result, it requires significant compute resources in post-training phase. To overcome these limitations, in this work, we propose Semantic Soft Bootstrapping (SSB), a self-distillation technique, in which the same base language model plays the role of both teacher and student, but receives different semantic contexts about the correctness of its outcome at training time. The model is first prompted with a math problem and several rollouts are generated. From them, the correct and most common incorrect response are filtered, and then provided to the model in context to produce a more robust, step-by-step explanation with a verified final answer. This pipeline automatically curates a paired teacher-student training set from raw problem-answer data, without any human intervention. This generation process also produces a sequence of logits, which is what the student model tries to match in the training phase just from the bare question alone. In our experiment, Qwen2.5-3B-Instruct on GSM8K dataset via parameter-efficient fine-tuning. We then tested its accuracy on MATH500, and AIME2024 benchmarks. Our experiments show a jump of 10.6%, and 10% improvements in accuracy, respectively, over group relative policy optimization (GRPO), which is a commonly used RLVR algorithm. Our code is available at https://github.com/purbeshmitra/semantic-soft-bootstrapping, and the model, curated dataset is available at https://huggingface.co/purbeshmitra/semantic-soft-bootstrapping.

Reinforcement learning in large language models (LLMs) often relies on scalar rewards, a practice that discards valuable textual rationale buried in the rollouts, forcing the model to explore de novo with each attempt and hindering sample efficiency. While LLMs can uniquely learn from language feedback provided in-context, naively integrating on-line experiences into RL training presents a paradox: feedback from the same problem risks information leakage and memorization, while feedback from different problems often leads to behavior collapse due to irrelevant context. To resolve this tension, we propose Language-And-Numerical Policy Optimization (LANPO), a framework that cleanly separates the roles of feedback: language guides exploration, while numerical rewards drive optimization. LANPO builds a dynamic experience pool from past trials and introduces two principles to ensure feedback is effective: Reward-Agnostic Reflection for safe intra-sample self-correction and Relevant Abstraction to distill generalizable lessons from inter-sample experiences. Across mathematical reasoning benchmarks, LANPO enables 7B and 14B models to significantly outperform strong baselines trained with GRPO in test accuracy. Our work provides a robust method for integrating historical experiences into the LLM RL loop, creating more effective and data-efficient learning agents.

Vision-Language Models (VLMs) excel in many direct multimodal tasks but struggle to translate this prowess into effective decision-making within interactive, visually rich environments like games. This ``knowing-doing'' gap significantly limits their potential as autonomous agents, as leading VLMs often performing badly in simple games. To address this, we introduce VLM-Gym, a curated reinforcement learning (RL) environment featuring diverse visual games with unified interfaces and adjustable, compositional difficulty, specifically designed for scalable multi-game parallel training. Leveraging VLM-Gym, we train G0 models using pure RL-driven self-evolution, which demonstrate emergent perception and reasoning patterns. To further mitigate challenges arising from game diversity, we develop G1 models. G1 incorporates a perception-enhanced cold start prior to RL fine-tuning. Our resulting G1 models consistently surpass their teacher across all games and outperform leading proprietary models like Claude-3.7-Sonnet-Thinking. Systematic analysis reveals an intriguing finding: perception and reasoning abilities mutually bootstrap each other throughout the RL training process. Source code including VLM-Gym and RL training are released at https://github.com/chenllliang/G1 to foster future research in advancing VLMs as capable interactive agents.

Large language models (LLMs) are powerful dialogue agents, but specializing them towards fulfilling a specific function can be challenging. Instructing tuning, i.e. tuning models on instruction and sample responses generated by humans (Ouyang et al., 2022), has proven as an effective method to do so, yet requires a number of data samples that a) might not be available or b) costly to generate. Furthermore, this cost increases when the goal is to make the LLM follow a specific workflow within a dialogue instead of single instructions. Inspired by the self-play technique in reinforcement learning and the use of LLMs to simulate human agents, we propose a more effective method for data collection through LLMs engaging in a conversation in various roles. This approach generates a training data via "self-talk" of LLMs that can be refined and utilized for supervised fine-tuning. We introduce an automated way to measure the (partial) success of a dialogue. This metric is used to filter the generated conversational data that is fed back in LLM for training. Based on our automated and human evaluations of conversation quality, we demonstrate that such self-talk data improves results. In addition, we examine the various characteristics that showcase the quality of generated dialogues and how they can be connected to their potential utility as training data.

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.

Preference-based reinforcement learning (PbRL) aligns a robot behavior with human preferences via a reward function learned from binary feedback over agent behaviors. We show that dynamics-aware reward functions improve the sample efficiency of PbRL by an order of magnitude. In our experiments we iterate between: (1) learning a dynamics-aware state-action representation (z^{sa}) via a self-supervised temporal consistency task, and (2) bootstrapping the preference-based reward function from (z^{sa}), which results in faster policy learning and better final policy performance. For example, on quadruped-walk, walker-walk, and cheetah-run, with 50 preference labels we achieve the same performance as existing approaches with 500 preference labels, and we recover 83\% and 66\% of ground truth reward policy performance versus only 38\% and 21\%. The performance gains demonstrate the benefits of explicitly learning a dynamics-aware reward model. Repo: https://github.com/apple/ml-reed.

Offline goal-conditioned reinforcement learning (GCRL) is a promising approach for pretraining generalist policies on large datasets of reward-free trajectories, akin to the self-supervised objectives used to train foundation models for computer vision and natural language processing. However, scaling GCRL to longer horizons remains challenging due to the combination of sparse rewards and discounting, which obscures the comparative advantages of primitive actions with respect to distant goals. Hierarchical RL methods achieve strong empirical results on long-horizon goal-reaching tasks, but their reliance on modular, timescale-specific policies and subgoal generation introduces significant additional complexity and hinders scaling to high-dimensional goal spaces. In this work, we introduce an algorithm to train a flat (non-hierarchical) goal-conditioned policy by bootstrapping on subgoal-conditioned policies with advantage-weighted importance sampling. Our approach eliminates the need for a generative model over the (sub)goal space, which we find is key for scaling to high-dimensional control in large state spaces. We further show that existing hierarchical and bootstrapping-based approaches correspond to specific design choices within our derivation. Across a comprehensive suite of state- and pixel-based locomotion and manipulation benchmarks, our method matches or surpasses state-of-the-art offline GCRL algorithms and scales to complex, long-horizon tasks where prior approaches fail. Project page: https://johnlyzhou.github.io/saw/

Recent advances have demonstrated the effectiveness of Reinforcement Learning (RL) in improving the reasoning capabilities of Large Language Models (LLMs). However, existing works inevitably rely on high-quality instructions and verifiable rewards for effective training, both of which are often difficult to obtain in specialized domains. In this paper, we propose Self-play Reinforcement Learning(SeRL) to bootstrap LLM training with limited initial data. Specifically, SeRL comprises two complementary modules: self-instruction and self-rewarding. The former module generates additional instructions based on the available data at each training step, employing robust online filtering strategies to ensure instruction quality, diversity, and difficulty. The latter module introduces a simple yet effective majority-voting mechanism to estimate response rewards for additional instructions, eliminating the need for external annotations. Finally, SeRL performs conventional RL based on the generated data, facilitating iterative self-play learning. Extensive experiments on various reasoning benchmarks and across different LLM backbones demonstrate that the proposed SeRL yields results superior to its counterparts and achieves performance on par with those obtained by high-quality data with verifiable rewards. Our code is available at https://github.com/wantbook-book/SeRL.

Reinforcement Learning from Verifiable Rewards (RLVR) suffers from exploration inefficiency, where models struggle to generate successful rollouts, resulting in minimal learning signal. This challenge is particularly severe for tasks that require the acquisition of novel reasoning patterns or domain-specific knowledge. To address this, we propose Context Bootstrapped Reinforcement Learning (CBRL), which augments RLVR training by stochastically prepending few-shot demonstrations to training prompts. The injection probability follows a curriculum that starts high to bootstrap early exploration, then anneals to zero so the model must ultimately succeed without assistance. This forces the policy to internalize reasoning patterns from the demonstrations rather than relying on them at test time. We validate CBRL across two model families and five Reasoning Gym tasks. Our results demonstrate that CBRL consistently improves success rate, provides better exploration efficiency, and is algorithm-agnostic. We further demonstrate CBRL's practical applicability on Q, a domain-specific programming language that diverges significantly from mainstream language conventions.

We propose a method for meta-learning reinforcement learning algorithms by searching over the space of computational graphs which compute the loss function for a value-based model-free RL agent to optimize. The learned algorithms are domain-agnostic and can generalize to new environments not seen during training. Our method can both learn from scratch and bootstrap off known existing algorithms, like DQN, enabling interpretable modifications which improve performance. Learning from scratch on simple classical control and gridworld tasks, our method rediscovers the temporal-difference (TD) algorithm. Bootstrapped from DQN, we highlight two learned algorithms which obtain good generalization performance over other classical control tasks, gridworld type tasks, and Atari games. The analysis of the learned algorithm behavior shows resemblance to recently proposed RL algorithms that address overestimation in value-based methods.

Meta-learning empowers artificial intelligence to increase its efficiency by learning how to learn. Unlocking this potential involves overcoming a challenging meta-optimisation problem. We propose an algorithm that tackles this problem by letting the meta-learner teach itself. The algorithm first bootstraps a target from the meta-learner, then optimises the meta-learner by minimising the distance to that target under a chosen (pseudo-)metric. Focusing on meta-learning with gradients, we establish conditions that guarantee performance improvements and show that the metric can control meta-optimisation. Meanwhile, the bootstrapping mechanism can extend the effective meta-learning horizon without requiring backpropagation through all updates. We achieve a new state-of-the art for model-free agents on the Atari ALE benchmark and demonstrate that it yields both performance and efficiency gains in multi-task meta-learning. Finally, we explore how bootstrapping opens up new possibilities and find that it can meta-learn efficient exploration in an epsilon-greedy Q-learning agent, without backpropagating through the update rule.

We propose BOSS, an approach that automatically learns to solve new long-horizon, complex, and meaningful tasks by growing a learned skill library with minimal supervision. Prior work in reinforcement learning require expert supervision, in the form of demonstrations or rich reward functions, to learn long-horizon tasks. Instead, our approach BOSS (BOotStrapping your own Skills) learns to accomplish new tasks by performing "skill bootstrapping," where an agent with a set of primitive skills interacts with the environment to practice new skills without receiving reward feedback for tasks outside of the initial skill set. This bootstrapping phase is guided by large language models (LLMs) that inform the agent of meaningful skills to chain together. Through this process, BOSS builds a wide range of complex and useful behaviors from a basic set of primitive skills. We demonstrate through experiments in realistic household environments that agents trained with our LLM-guided bootstrapping procedure outperform those trained with naive bootstrapping as well as prior unsupervised skill acquisition methods on zero-shot execution of unseen, long-horizon tasks in new environments. Website at clvrai.com/boss.

Many classic Reinforcement Learning (RL) algorithms rely on a Bellman operator, which involves an expectation over the next states, leading to the concept of bootstrapping. To introduce a form of pessimism, we propose to replace this expectation with an expectile. In practice, this can be very simply done by replacing the L_2 loss with a more general expectile loss for the critic. Introducing pessimism in RL is desirable for various reasons, such as tackling the overestimation problem (for which classic solutions are double Q-learning or the twin-critic approach of TD3) or robust RL (where transitions are adversarial). We study empirically these two cases. For the overestimation problem, we show that the proposed approach, ExpectRL, provides better results than a classic twin-critic. On robust RL benchmarks, involving changes of the environment, we show that our approach is more robust than classic RL algorithms. We also introduce a variation of ExpectRL combined with domain randomization which is competitive with state-of-the-art robust RL agents. Eventually, we also extend \ExpectRL with a mechanism for choosing automatically the expectile value, that is the degree of pessimism

Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old sampling FLOPs (from prior inference or RL training) in the form of off-policy traces. Standard off-policy methods supervise against off-policy data, causing instabilities during RL optimization. We introduce PrefixRL, where we condition on the prefix of successful off-policy traces and run on-policy RL to complete them, side-stepping off-policy instabilities. PrefixRL boosts the learning signal on hard problems by modulating the difficulty of the problem through the off-policy prefix length. We prove that the PrefixRL objective is not only consistent with the standard RL objective but also more sample efficient. Empirically, we discover back-generalization: training only on prefixed problems generalizes to out-of-distribution unprefixed performance, with learned strategies often differing from those in the prefix. In our experiments, we source the off-policy traces by rejection sampling with the base model, creating a self-improvement loop. On hard reasoning problems, PrefixRL reaches the same training reward 2x faster than the strongest baseline (SFT on off-policy data then RL), even after accounting for the compute spent on the initial rejection sampling, and increases the final reward by 3x. The gains transfer to held-out benchmarks, and PrefixRL is still effective when off-policy traces are derived from a different model family, validating its flexibility in practical settings.

Interactive tool-using agents must solve real-world tasks via multi-turn interaction with both humans and external environments, requiring dialogue state tracking, multi-step tool execution, while following complex instructions. Post-training such agents is challenging because synthesis for high-quality multi-turn tool-use data is difficult to scale, and reinforcement learning (RL) could face noisy signals caused by user simulation, leading to degraded training efficiency. We propose a unified framework that combines a self-evolving data agent with verifier-based RL. Our system, EigenData, is a hierarchical multi-agent engine that synthesizes tool-grounded dialogues together with executable per-instance checkers, and improves generation reliability via closed-loop self-evolving process that updates prompts and workflow. Building on the synthetic data, we develop an RL recipe that first fine-tunes the user model and then applies GRPO-style training with trajectory-level group-relative advantages and dynamic filtering, yielding consistent improvements beyond SFT. Evaluated on tau^2-bench, our best model reaches 73.0% pass^1 on Airline and 98.3% pass^1 on Telecom, matching or exceeding frontier models. Overall, our results suggest a scalable pathway for bootstrapping complex tool-using behaviors without expensive human annotation.

Diffusion-based Q-learning has emerged as a powerful paradigm for offline reinforcement learning, but its reliance on multi-step denoising makes both training and inference computationally expensive and brittle. Recent efforts to accelerate diffusion Q-learning toward single-step action generation typically introduce auxiliary networks, policy distillation, or multi-phase training, which frequently compromise simplicity, stability, or performance. To address these limitations, we introduce Bootstrapped Flow Q-Learning (BFQ), a novel framework that enables accurate single-step action generation during both training and inference, without auxiliary networks or distillation procedures. BFQ adopts a divide-and-conquer view of the displacement vector along the flow path: it begins by learning short-range displacements that can be accurately estimated from the Flow Matching marginal velocity, and bootstraps these components to directly learn a noise-to-action mapping in a single step. This formulation eliminates multi-step denoising, resulting in a learning procedure that is substantially faster, simpler, and more robust. Extensive D4RL evaluations show that BFQ improves performance while significantly reducing computational cost compared to multi-step diffusion baselines, demonstrating that single-step action generation suffices for high-performance offline Reinforcement Learning.

Off-policy, value-based reinforcement learning methods such as Q-learning are appealing because they can learn from arbitrary experience, including data collected by older policies or other agents. In practice, however, bootstrapping makes long-horizon learning brittle: estimation errors at later states propagate backward through temporal-difference (TD) updates and can compound over time. We propose long-horizon Q-learning (LQL), which introduces a principled backstop against compounding error when learning the optimal action-value function. LQL builds on a prior optimality tightening observation: any realized action sequence lower-bounds what the optimal policy can achieve in expectation, so acting optimally earlier should not be worse than following the observed actions for several steps before switching to optimal behavior. Our contribution is to turn this inequality into a practical stabilization mechanism for Q-learning by using a hinge loss to penalize violations of these bounds. Importantly, LQL computes these penalties using network outputs already produced for the TD error, requiring no auxiliary networks and no additional forward passes relative to Q-learning. When combined with multiple state-of-the-art methods on a range of online and offline-to-online benchmarks, LQL consistently outperforms both 1-step TD and n-step TD learning at similar runtime.

Pretraining navigation diffusion policies rely on large-scale expert demonstrations. These data are typically generated by a fully-informed oracle planner suited to a single nominal robot. This limits the policy's generalization to diverse embodiments and challenging scenarios (e.g., escaping dead ends or detouring long obstacles) that demand diverse local reactive behaviors with only onboard local observations. Post-training the policy with reinforcement learning (RL) offers a principled remedy. However, previous RL for diffusion approaches lead to only marginal improvements. This is because the intractable likelihood of diffusion policies renders policy gradients unstable in addition to inefficient policy exploration. To address these challenges, we propose a data-efficient diffusion RL post-training framework - GQRM (Group Q-score Reweighted Matching). Our framework introduces two complementary designs: (i) a self-bootstrapped exploration strategy with behavior perturbation that preserves the pretrained policy prior, and (ii) a group Q-score normalization mechanism that computes per-trajectory values on each state for efficient reweighted score matching. By conducting distributed online RL training across heterogeneous embodiments, the resulting fine-tuned policy, X-NavDP, achieves state-of-the-art cross-embodiment visual navigation performance, improving the overall success rate from 61.20% to 84.28% in simulation and 10% to 65% in real-world hard cases. The code and model are publicly available at https://yty-sky.github.io/x-navdp-project-page.

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

Reinforcement Learning (RL) with rubric-based rewards has recently shown remarkable progress in enhancing general reasoning capabilities of Large Language Models (LLMs), yet still suffers from ineffective exploration confined to curent policy distribution. In fact, RL optimization can be viewed as steering the policy toward an ideal distribution that maximizes the rewards, while effective exploration should align efforts with desired target. Leveraging this insight, we propose HeRL, a Hindsight experience guided Reinforcement Learning framework to bootstrap effective exploration by explicitly telling LLMs the desired behaviors specified in rewards. Concretely, HeRL treats failed trajectories along with their unmet rubrics as hindsight experience, which serves as in-context guidance for the policy to explore desired responses beyond its current distribution. Additionally, we introduce a bonus reward to incentivize responses with greater potential for improvement under such guidance. HeRL facilitates effective learning from desired high quality samples without repeated trial-and-error from scratch, yielding a more accurate estimation of the expected gradient theoretically. Extensive experiments across various benchmarks demonstrate that HeRL achieves superior performance gains over baselines, and can further benefit from experience guided self-improvement at test time. Our code is available at https://github.com/sikelifei/HeRL.

We show that Reinforcement Learning (RL) methods for solving Text-Based Games (TBGs) often fail to generalize on unseen games, especially in small data regimes. To address this issue, we propose Context Relevant Episodic State Truncation (CREST) for irrelevant token removal in observation text for improved generalization. Our method first trains a base model using Q-learning, which typically overfits the training games. The base model's action token distribution is used to perform observation pruning that removes irrelevant tokens. A second bootstrapped model is then retrained on the pruned observation text. Our bootstrapped agent shows improved generalization in solving unseen TextWorld games, using 10x-20x fewer training games compared to previous state-of-the-art methods despite requiring less number of training episodes.

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real data experiments, we show the generality and adaptivity of MBE.

As systems trend toward superintelligence, a natural modeling premise is that agents can self-improve along every facet of their own design. We formalize this with a five-axis decomposition and a decision layer, separating incentives from learning behavior and analyzing axes in isolation. Our central result identifies and introduces a sharp utility--learning tension, the structural conflict in self-modifying systems whereby utility-driven changes that improve immediate or expected performance can also erode the statistical preconditions for reliable learning and generalization. Our findings show that distribution-free guarantees are preserved iff the policy-reachable model family is uniformly capacity-bounded; when capacity can grow without limit, utility-rational self-changes can render learnable tasks unlearnable. Under standard assumptions common in practice, these axes reduce to the same capacity criterion, yielding a single boundary for safe self-modification. Numerical experiments across several axes validate the theory by comparing destructive utility policies against our proposed two-gate policies that preserve learnability.

Offline reinforcement learning restricts the learning process to rely only on logged-data without access to an environment. While this enables real-world applications, it also poses unique challenges. One important challenge is dealing with errors caused by the overestimation of values for state-action pairs not well-covered by the training data. Due to bootstrapping, these errors get amplified during training and can lead to divergence, thereby crippling learning. To overcome this challenge, we introduce Regularized Behavior Value Estimation (R-BVE). Unlike most approaches, which use policy improvement during training, R-BVE estimates the value of the behavior policy during training and only performs policy improvement at deployment time. Further, R-BVE uses a ranking regularisation term that favours actions in the dataset that lead to successful outcomes. We provide ample empirical evidence of R-BVE's effectiveness, including state-of-the-art performance on the RL Unplugged ATARI dataset. We also test R-BVE on new datasets, from bsuite and a challenging DeepMind Lab task, and show that R-BVE outperforms other state-of-the-art discrete control offline RL methods.

Large language models (LLMs) excel at reasoning, yet post-training remains critical for aligning their behavior with task goals. Existing reinforcement learning (RL) methods often depend on costly human annotations or external reward models. We propose Reinforcement Learning via Self-Confidence (RLSC), which uses the model's own confidence as reward signals-eliminating the need for labels, preference models, or reward engineering. Applied to Qwen2.5-Math-7B with only 16 samples per question and 10 or 20 training steps, RLSC improves accuracy by +13.4% on AIME2024, +21.2% on MATH500, +21.7% on Minerva Math, +20.8% on Olympiadbench, and +9.7% on AMC23. RLSC provides a simple, scalable post-training method for inference models, requiring only a small number of samples and unlabelled supervision.

Large language models (LLMs) are becoming the foundation for autonomous agents that can use tools to solve complex tasks. Reinforcement learning (RL) has emerged as a common approach for injecting such agentic capabilities, but typically under tightly controlled training setups. It often depends on carefully constructed task-solution pairs and substantial human supervision, which creates a fundamental obstacle to open-ended self-evolution toward superintelligent systems. In this paper, we propose Tool-R0 framework for training general purpose tool-calling agents from scratch with self-play RL, under a zero-data assumption. Initialized from the same base LLM, Tool-R0 co-evolves a Generator and a Solver with complementary rewards: one proposes targeted challenging tasks at the other's competence frontier and the other learns to solve them with real-world tool calls. This creates a self-evolving cycle that requires no pre-existing tasks or datasets. Evaluation on different tool-use benchmarks show that Tool-R0 yields 92.5 relative improvement over the base model and surpasses fully supervised tool-calling baselines under the same setting. Our work further provides empirical insights into self-play LLM agents by analyzing co-evolution, curriculum dynamics, and scaling behavior.

We propose Heuristic Blending (HUBL), a simple performance-improving technique for a broad class of offline RL algorithms based on value bootstrapping. HUBL modifies the Bellman operators used in these algorithms, partially replacing the bootstrapped values with heuristic ones that are estimated with Monte-Carlo returns. For trajectories with higher returns, HUBL relies more on the heuristic values and less on bootstrapping; otherwise, it leans more heavily on bootstrapping. HUBL is very easy to combine with many existing offline RL implementations by relabeling the offline datasets with adjusted rewards and discount factors. We derive a theory that explains HUBL's effect on offline RL as reducing offline RL's complexity and thus increasing its finite-sample performance. Furthermore, we empirically demonstrate that HUBL consistently improves the policy quality of four state-of-the-art bootstrapping-based offline RL algorithms (ATAC, CQL, TD3+BC, and IQL), by 9% on average over 27 datasets of the D4RL and Meta-World benchmarks.

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

In this paper we introduce a new unsupervised reinforcement learning method for discovering the set of intrinsic options available to an agent. This set is learned by maximizing the number of different states an agent can reliably reach, as measured by the mutual information between the set of options and option termination states. To this end, we instantiate two policy gradient based algorithms, one that creates an explicit embedding space of options and one that represents options implicitly. The algorithms also provide an explicit measure of empowerment in a given state that can be used by an empowerment maximizing agent. The algorithm scales well with function approximation and we demonstrate the applicability of the algorithm on a range of tasks.

Language models often struggle to follow multi-constraint instructions that are crucial for real-world applications. Existing reinforcement learning (RL) approaches suffer from dependency on external supervision and sparse reward signals from multi-constraint tasks. We propose a label-free self-supervised RL framework that eliminates dependency on external supervision by deriving reward signals directly from instructions and generating pseudo-labels for reward model training. Our approach introduces constraint decomposition strategies and efficient constraint-wise binary classification to address sparse reward challenges while maintaining computational efficiency. Experiments show that our approach generalizes well, achieving strong improvements across 3 in-domain and 5 out-of-domain datasets, including challenging agentic and multi-turn instruction following. The data and code are publicly available at https://github.com/Rainier-rq/verl-if

While Reinforcement Learning for Verifiable Rewards (RLVR) is powerful for training large reasoning models, its training dynamics harbor a critical challenge: RL overfitting, where models gain training rewards but lose generalization. Our analysis reveals this is driven by policy over-specialization and catastrophic forgetting of diverse solutions generated during training. Standard optimization discards this valuable inter-step policy diversity. To address this, we introduce RLoop, a self-improving framework built on iterative policy initialization. RLoop transforms the standard training process into a virtuous cycle: it first uses RL to explore the solution space from a given policy, then filters the successful trajectories to create an expert dataset. This dataset is used via Rejection-sampling Fine-Tuning (RFT) to refine the initial policy, creating a superior starting point for the next iteration. This loop of exploration and exploitation via iterative re-initialization effectively converts transient policy variations into robust performance gains. Our experiments show RLoop mitigates forgetting and substantially improves generalization, boosting average accuracy by 9% and pass@32 by over 15% compared to vanilla RL.

We present AutoResearch-RL, a framework in which a reinforcement learning agent conducts open-ended neural architecture and hyperparameter research without human supervision, running perpetually until a termination oracle signals convergence or resource exhaustion. At each step the agent proposes a code modification to a target training script, executes it under a fixed wall clock time budget, observes a scalar reward derived from validation bits-per-byte (val-bpb), and updates its policy via Proximal Policy Optimisation (PPO). The key design insight is the separation of three concerns: (i) a frozen environment (data pipeline, evaluation protocol, and constants) that guarantees fair cross-experiment comparison; (ii) a mutable target file (train.py) that represents the agent's editable state; and (iii) a meta-learner (the RL agent itself) that accumulates a growing trajectory of experiment outcomes and uses them to inform subsequent proposals. We formalise this as a Markov Decision Process, derive convergence guarantees under mild assumptions, and demonstrate empirically on a single GPU nanochat pretraining benchmark that AutoResearch-RL discovers configurations that match or exceed hand-tuned baselines after approximately 300 overnight iterations, with no human in the loop.

In the same way that the computer vision (CV) and natural language processing (NLP) communities have developed self-supervised methods, reinforcement learning (RL) can be cast as a self-supervised problem: learning to reach any goal, without requiring human-specified rewards or labels. However, actually building a self-supervised foundation for RL faces some important challenges. Building on prior contrastive approaches to this RL problem, we conduct careful ablation experiments and discover that a shallow and wide architecture, combined with careful weight initialization and data augmentation, can significantly boost the performance of these contrastive RL approaches on challenging simulated benchmarks. Additionally, we demonstrate that, with these design decisions, contrastive approaches can solve real-world robotic manipulation tasks, with tasks being specified by a single goal image provided after training.

We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap programme. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tri-critical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global so(2,2) part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the non-perturbative structure of arbitrary (unitary or non-unitary) CFTs.

Reinforcement learning (RL) has emerged as a central paradigm for post-training LLM agents, yet its trajectory-level reward signal provides only coarse supervision for long-horizon interaction. On-Policy Self-Distillation (OPSD) complements RL by introducing dense token-level guidance from a teacher branch augmented with privileged context. However, transferring OPSD to multi-turn agents proves problematic: compounding multi-turn instability destabilizes supervision, while skill-conditioned privileged guidance requires asymmetric treatment for negative teacher rejections may arise from imperfect skills retrieval or utilization. We introduce SDAR (Self-Distilled Agentic Reinforcement Learning), which treats OPSD as a gated auxiliary objective while keeping RL as the primary optimization backbone. SDAR maps detached token-level signals into a sigmoid gate, strengthening distillation on teacher-endorsed positive-gap tokens and softly attenuating negative teacher rejections. Across the Qwen2.5 and Qwen3 families on ALFWorld, WebShop, and Search-QA, SDAR substantially improves over GRPO (+9.4% on ALFWorld, +7.0% on Search-QA, +10.2% on WebShop-Acc), avoids the instability of naive GRPO+OPSD, and consistently outperforms hybrid RL--OPSD baselines across model scales.

Self-play with large language models has emerged as a promising paradigm for achieving self-improving artificial intelligence. However, existing self-play frameworks often suffer from optimization instability, due to (i) non-stationary objectives induced by solver-dependent reward feedback for the Questioner, and (ii) bootstrapping errors from self-generated pseudo-labels used to supervise the Solver. To mitigate these challenges, we introduce DARC (Decoupled Asymmetric Reasoning Curriculum), a two-stage framework that stabilizes the self-evolution process. First, we train the Questioner to synthesize difficulty-calibrated questions, conditioned on explicit difficulty levels and external corpora. Second, we train the Solver with an asymmetric self-distillation mechanism, where a document-augmented teacher generates high-quality pseudo-labels to supervise the student Solver that lacks document access. Empirical results demonstrate that DARC is model-agnostic, yielding an average improvement of 10.9 points across nine reasoning benchmarks and three backbone models. Moreover, DARC consistently outperforms all baselines and approaches the performance of fully supervised models without relying on human annotations.The code is available at https://github.com/RUCBM/DARC.

Large Language Models (LLMs) often produce plausible but poorly-calibrated answers, limiting their reliability on reasoning-intensive tasks. We present Reinforcement Learning from Self-Feedback (RLSF), a post-training stage that uses the model's own confidence as an intrinsic reward, mimicking how humans learn in the absence of external feedback. After a frozen LLM generates several chain-of-thought solutions, we define and compute the confidence of each final answer span and rank the traces accordingly. These synthetic preferences are then used to fine-tune the policy with standard preference optimization, similar to RLHF yet requiring no human labels, gold answers, or externally curated rewards. RLSF simultaneously (i) refines the model's probability estimates -- restoring well-behaved calibration -- and (ii) strengthens step-by-step reasoning, yielding improved performance on arithmetic reasoning and multiple-choice question answering. By turning a model's own uncertainty into useful self-feedback, RLSF affirms reinforcement learning on intrinsic model behaviour as a principled and data-efficient component of the LLM post-training pipeline and warrents further research in intrinsic rewards for LLM post-training.

Training large language models (LLMs) for complex reasoning via Reinforcement Learning with Verifiable Rewards (RLVR) is effective but limited by reliance on costly, domain-specific supervision. We explore Reinforcement Learning from Internal Feedback (RLIF), a framework that enables LLMs to learn from intrinsic signals without external rewards or labeled data. We propose Intuitor, an RLIF method that uses a model's own confidence, termed self-certainty, as its sole reward signal. Intuitor replaces external rewards in Group Relative Policy Optimization (GRPO) with self-certainty scores, enabling fully unsupervised learning. Experiments demonstrate that Intuitor matches GRPO's performance on mathematical benchmarks while achieving superior generalization to out-of-domain tasks like code generation, without requiring gold solutions or test cases. Our findings show that intrinsic model signals can drive effective learning across domains, offering a scalable alternative to RLVR for autonomous AI systems where verifiable rewards are unavailable. Code is available at https://github.com/sunblaze-ucb/Intuitor

Large reasoning models often solve problems through long chain-of-thought (CoT) traces, yet much of this computation is spent on redundant derivations, repeated self-verification, and detours that do not improve the final answer. Existing on-policy self-distillation methods reduce this cost by matching a student model to a concise copy of itself on prefixes sampled from the student's own rollouts. We show that this objective has an initialization bottleneck. Since supervision is applied only to visited prefixes, training from a verbose base model places the KL loss on contexts that are often noisy, redundant, or already off track. In such regions, a concise teacher can provide only local corrections, while the student continues to explore trajectories that an efficient reasoner should avoid. In this paper, we propose BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training. BIRD first samples concise solutions from the base model under a brevity instruction, keeps only answer-correct traces, and performs a lightweight prompt-switch SFT step. The traces are generated with the brevity instruction but learned under the original task prompt, turning instruction-induced conciseness into a default reasoning behavior. Starting from this warm model, BIRD then applies on-policy reverse-KL distillation with a concise self-teacher, now on cleaner and more informative prefixes. Across Qwen3 series models, BIRD achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while reducing the average response length from 3,099 to 1,115 tokens. These results highlight prefix support as a central factor in efficient reasoning distillation.

In reinforcement learning, the advantage function is critical for policy improvement, but is often extracted from a learned Q-function. A natural question is: Why not learn the advantage function directly? In this work, we introduce VA-learning, which directly learns advantage function and value function using bootstrapping, without explicit reference to Q-functions. VA-learning learns off-policy and enjoys similar theoretical guarantees as Q-learning. Thanks to the direct learning of advantage function and value function, VA-learning improves the sample efficiency over Q-learning both in tabular implementations and deep RL agents on Atari-57 games. We also identify a close connection between VA-learning and the dueling architecture, which partially explains why a simple architectural change to DQN agents tends to improve performance.

Scaling the performance of large language models (LLMs) increasingly depends on methods that reduce reliance on human supervision. Reinforcement learning from automated verification offers an alternative, but it incurs scalability limitations due to dependency upon human-designed verifiers. Self-training, where the model's own judgment provides the supervisory signal, presents a compelling direction. We propose an online self-training reinforcement learning algorithm that leverages the model's self-consistency to infer correctness signals and train without any ground-truth supervision. We apply the algorithm to challenging mathematical reasoning tasks and show that it quickly reaches performance levels rivaling reinforcement-learning methods trained explicitly on gold-standard answers. Additionally, we analyze inherent limitations of the algorithm, highlighting how the self-generated proxy reward initially correlated with correctness can incentivize reward hacking, where confidently incorrect outputs are favored. Our results illustrate how self-supervised improvement can achieve significant performance gains without external labels, while also revealing its fundamental challenges.

The effectiveness of Reinforcement Learning (RL) in Large Language Models (LLMs) depends on the nature and diversity of the data used before and during RL. In particular, reasoning problems can often be approached in multiple ways that rely on different forms of reasoning, and exposure to only a limited range of such approaches in the training data may limit the effectiveness of RL. Motivated by this, we investigate using diverse self-generated data during mid-training as an intermediate step before RL training. Specifically, we adopt a bootstrapped data-generation framework guided by George Polya's problem-solving approaches for generating multiple variants of correct answers for each question in the training data, and then perform fine-tuning. We first provide a theoretical perspective on how mid-training on such data improves RL and explain how policy-gradient updates can incentivize combining multiple approaches. We then empirically demonstrate that RL-trained models initialized with our mid-training data achieve consistent improvements across various mathematical reasoning benchmarks and other OOD tasks like code generation and narrative reasoning. Overall, our investigative study shows that a language model learning multiple problem-solving approaches, through self-generated data helps subsequent RL.

Large language model (LLM) agents learn by interacting with environments, but long-horizon training remains fundamentally bottlenecked by sparse and delayed rewards. Existing methods typically address this challenge through post-hoc credit assignment or external reward models, which provide limited guidance at inference time and often separate reward improvement from policy improvement. We propose Self-Guide, a self-generated internal reward for language agents that supports both inference-time guidance and training-time supervision. Specifically, the agent uses Self-Guide as a short self-guidance signal to steer the next action during inference, and converts the same signal into step-level internal reward for denser policy optimization during training. This creates a co-evolving loop: better policy produces better guidance, and better guidance further improves policy as internal reward. Across three agent benchmarks, inference-time self-guidance already yields clear gains, while jointly evolving policy and internal reward with GRPO brings further improvements (8\%) over baselines trained solely with environment reward. Overall, our results suggest that language agents can improve not only by collecting more experience, but also by learning to generate and refine their own internal reward during acting and learning.

Reinforcement learning (RL) has emerged as a powerful approach for improving reasoning in language and vision-language models, yet its strongest successes still depend heavily on ground-truth supervision (e.g., verifiable reward). Such annotations are costly to obtain and become increasingly scarce as reasoning capabilities advance beyond what humans can reliably evaluate. Self-rewarding RL reduces this dependence by enabling models to derive reward signals from their own completions. However, training solely on self-generated feedback can reinforce existing biases and suboptimal behaviors, reduce response diversity, and ultimately lead to homogenized responses and training collapse. In this work, we show that unsupervised reasoning can emerge through cooperative multi-agent training. We introduce Co-RL, a framework in which multiple decoupled models, sharing no parameters, are simultaneously optimized through RL using rewards derived from their peers. We further show that increasing cohort diversity, through heterogeneous model families, sizes, and rephrased training samples, reduces the correlated errors that drive self-reinforcing feedback loops. This diversity consistently improves reasoning performance, maintains behavioral diversity, and mitigates training collapse. Across text-only and multimodal domains, Co-RL consistently outperforms the base models and prior label-free approaches, while matching or surpassing supervised methods, without access to any ground-truth labels. Concretely, Co-RL yields average gains of 3.0-8.6% across seven text-only benchmarks for LLMs and 2.3-7.2% across four multimodal benchmarks for VLMs. Code is available at https://github.com/DrStranded/Co-RL.

Reinforcement learning (RL) provides a theoretical framework for continuously improving an agent's behavior via trial and error. However, efficiently learning policies from scratch can be very difficult, particularly for tasks with exploration challenges. In such settings, it might be desirable to initialize RL with an existing policy, offline data, or demonstrations. However, naively performing such initialization in RL often works poorly, especially for value-based methods. In this paper, we present a meta algorithm that can use offline data, demonstrations, or a pre-existing policy to initialize an RL policy, and is compatible with any RL approach. In particular, we propose Jump-Start Reinforcement Learning (JSRL), an algorithm that employs two policies to solve tasks: a guide-policy, and an exploration-policy. By using the guide-policy to form a curriculum of starting states for the exploration-policy, we are able to efficiently improve performance on a set of simulated robotic tasks. We show via experiments that JSRL is able to significantly outperform existing imitation and reinforcement learning algorithms, particularly in the small-data regime. In addition, we provide an upper bound on the sample complexity of JSRL and show that with the help of a guide-policy, one can improve the sample complexity for non-optimism exploration methods from exponential in horizon to polynomial.

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.

Offline reinforcement learning aims to train agents from pre-collected datasets. However, this comes with the added challenge of estimating the value of behaviors not covered in the dataset. Model-based methods offer a potential solution by training an approximate dynamics model, which then allows collection of additional synthetic data via rollouts in this model. The prevailing theory treats this approach as online RL in an approximate dynamics model, and any remaining performance gap is therefore understood as being due to dynamics model errors. In this paper, we analyze this assumption and investigate how popular algorithms perform as the learned dynamics model is improved. In contrast to both intuition and theory, if the learned dynamics model is replaced by the true error-free dynamics, existing model-based methods completely fail. This reveals a key oversight: The theoretical foundations assume sampling of full horizon rollouts in the learned dynamics model; however, in practice, the number of model-rollout steps is aggressively reduced to prevent accumulating errors. We show that this truncation of rollouts results in a set of edge-of-reach states at which we are effectively ``bootstrapping from the void.'' This triggers pathological value overestimation and complete performance collapse. We term this the edge-of-reach problem. Based on this new insight, we fill important gaps in existing theory, and reveal how prior model-based methods are primarily addressing the edge-of-reach problem, rather than model-inaccuracy as claimed. Finally, we propose Reach-Aware Value Learning (RAVL), a simple and robust method that directly addresses the edge-of-reach problem and hence - unlike existing methods - does not fail as the dynamics model is improved. Code open-sourced at: github.com/anyasims/edge-of-reach.

Large Reasoning Models possess remarkable capabilities for self-correction in general domain; however, they frequently struggle to recover from unsafe reasoning trajectories under adversarial attacks. Existing alignment methods attempt to mitigate this vulnerability by fine-tuning the model on expert data including reflection traces or adversarial prefixes. Crucially, these approaches are often hindered by static training data which inevitably deviate from model's dynamic, on-policy reasoning traces, resulting in model hardly covering its vast generation space and learning to recover from its own failures. To bridge this gap, we propose Self-ReSET, a pure reinforcement learning framework designed to equip LRMs with the intrinsic capacity to recover from their own safety error trajectories, which are subsequently reused as an initial state for reinforcement learning. Extensive experiments across various LRMs and benchmarks demonstrate that Self-ReSET significantly enhances robustness against adversarial attacks especially out-of-distribution (OOD) jailbreak prompts while maintaining general utility, along with efficient data utilization. Further analysis reveals that our method effectively fosters self-recovery patterns, enabling models to better identify and recover from unsafe intermediate error states back to benign paths. Our codes and data are available at https://github.com/Ing1024/Self-ReSET.

Post-training has become the dominant recipe for turning a language model into a competent search-augmented reasoning agent. A line of recent work pushes its performance further by adding elaborate machinery on top of this standard pipeline. These augmentations import external supervision from stronger external systems, attach auxiliary modules such as process reward models or retrospective critics, restructure the rollout itself with tree search or multi-stage curricula, or shape the reward with hand-crafted bonuses and penalties. Each addition delivers a measurable gain, but each also inflates the training pipeline and ties the recipe to resources or designs that may not always be available. We take a step back and ask whether any of this machinery is actually necessary, and propose Search-E1, a self-evolution method that lets a search-augmented agent improve through only vanilla GRPO interleaved with on-policy self-distillation (OPSD). After each GRPO round, the policy rolls out on its own training questions. A token-level forward KL objective then aligns the policy's inference-time distribution to its own distribution under a privileged context that exposes a more efficient sibling trajectory. Despite this simplicity, the procedure naturally provides dense per-step supervision. On seven QA benchmarks, Search-E1 reaches 0.440 average EM with Qwen2.5-3B, surpassing all open-source baselines at both scales. Code and complete version will be made public soon.

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.

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.

LLMs are often trained with RL from human or AI feedback, yet such methods typically compress nuanced feedback into scalar rewards, discarding much of their richness and inducing scale imbalance. We propose treating verbal feedback as a conditioning signal. Inspired by language priors in text-to-image generation, which enable novel outputs from unseen prompts, we introduce the feedback-conditional policy (FCP). FCP learns directly from response-feedback pairs, approximating the feedback-conditional posterior through maximum likelihood training on offline data. We further develop an online bootstrapping stage where the policy generates under positive conditions and receives fresh feedback to refine itself. This reframes feedback-driven learning as conditional generation rather than reward optimization, offering a more expressive way for LLMs to directly learn from verbal feedback. Our code is available at https://github.com/sail-sg/feedback-conditional-policy.

Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL). Renowned for its convergence guarantees and stability compared to other RL algorithms, its practical application is often hindered by sensitivity to hyper-parameters, particularly the step-size. In this paper, we introduce the integration of the Polyak step-size in RL, which automatically adjusts the step-size without prior knowledge. To adapt this method to RL settings, we address several issues, including unknown f* in the Polyak step-size. Additionally, we showcase the performance of the Polyak step-size in RL through experiments, demonstrating faster convergence and the attainment of more stable policies.

Reinforcement learning (RL) has been widely used to train LLM agents for multi-turn interactive tasks, but its sample efficiency is severely limited by sparse rewards and long horizons. On-policy self-distillation (OPSD) alleviates this by providing dense token-level supervision from a privileged teacher that has access to ground-truth answers. However, such fixed privileged information cannot capture the diverse valid strategies in agent tasks, and naively combining OPSD with RL often leads to training collapse. To address these limitations, we introduce Skill-SD, a framework that turns the agent's own trajectories into dynamic training-only supervision. Completed trajectories are summarized into compact natural language skills that describe successful behaviors, mistakes, and workflows. These skills serve as dynamic privileged information conditioning only the teacher, while the student always acts under the plain task prompt and learns to internalize the guidance through distillation. To stabilize the training, we derive an importance-weighted reverse-KL loss to provide gradient-correct token-level distillation, and dynamically synchronize the teacher with the improving student. Experimental results on agentic benchmarks demonstrate that Skill-SD substantially outperforms the standard RL baseline, improving both vanilla GRPO (+14.0%/+10.9% on AppWorld/Sokoban) and vanilla OPD (+42.1%/+40.6%). Project page: https://k1xe.github.io/skill-sd/

Reinforcement learning has emerged as a paradigm for post-training large language models, boosting their reasoning capabilities. Such approaches compute an advantage value for each sample, reflecting better or worse performance than expected, thereby yielding both positive and negative signals for training. However, the indiscriminate mixing of the two signals in existing methods, especially from the early stages, may lead to ambiguous guidance and limited gains. To address this issue, we propose **CAPO** (**C**urriculum **A**dvantage **P**olicy **O**ptimization), an adaptive curriculum mechanism based on advantage signals. The proposed mechanism bootstraps imitation learning with positive-only advantage samples to establish robust foundations, and subsequently introduces negative signals to cultivate discriminative capabilities, thereby improving generalization across complex scenarios. Compatible with diverse optimization methods including GRPO, PPO, RLOO, and Reinforce++, our method consistently achieves stable and significant improvements in mathematical reasoning tasks, and further generalizes effectively to multimodal Graphical User Interface (GUI) reasoning scenarios, establishing itself as a versatile and robust optimization framework.

Model Predictive Control (MPC) has been demonstrated to be effective in continuous control tasks. When a world model and a value function are available, planning a sequence of actions ahead of time leads to a better policy. Existing methods typically obtain the value function and the corresponding policy in a model-free manner. However, we find that such an approach struggles with complex tasks, resulting in poor policy learning and inaccurate value estimation. To address this problem, we leverage the strengths of MPC itself. In this work, we introduce Bootstrapped Model Predictive Control (BMPC), a novel algorithm that performs policy learning in a bootstrapped manner. BMPC learns a network policy by imitating an MPC expert, and in turn, uses this policy to guide the MPC process. Combined with model-based TD-learning, our policy learning yields better value estimation and further boosts the efficiency of MPC. We also introduce a lazy reanalyze mechanism, which enables computationally efficient imitation learning. Our method achieves superior performance over prior works on diverse continuous control tasks. In particular, on challenging high-dimensional locomotion tasks, BMPC significantly improves data efficiency while also enhancing asymptotic performance and training stability, with comparable training time and smaller network sizes. Code is available at https://github.com/wertyuilife2/bmpc.

Contemporary reinforcement learning with verifiable reward methods post-train language models on multi-step reasoning by assigning a single outcome reward uniformly across all tokens in a trajectory. Such uniform assignment ignores which steps contributed to success or failure. Improving credit assignment can address this limitation by enabling targeted refinement of faulty reasoning steps, rather than updating entire trajectories uniformly. Resets are one such simple mechanism, enabling more precise credit assignment by returning to an intermediate state and resampling counterfactual continuations, so that outcome differences can be attributed to decisions made at that point. We propose two such methods: Random-Reset Policy Optimization (RRPO), where reset states are drawn randomly from reasoning steps, and Self-Reset Policy Optimization (SRPO), where the model self-localizes the erroneous step in an incorrect trajectory and resets there. We analyze these methods within the Conservative Policy Iteration (CPI) framework. Extending CPI with a credit-assignment oracle that targets improvable states yields provable improvements over random resets. Across models and reasoning benchmarks, SRPO consistently outperforms standard GRPO and RRPO by sampling multiple suffix continuations at a self-localized reset and learning from their rewards, using only the model itself with no external supervision.

We introduce Learning to Self-Evolve (LSE), a reinforcement learning framework that trains large language models (LLMs) to improve their own contexts at test time. We situate LSE in the setting of test-time self-evolution, where a model iteratively refines its context from feedback on seen problems to perform better on new ones. Existing approaches rely entirely on the inherent reasoning ability of the model and never explicitly train it for this task. LSE reduces the multi-step evolution problem to a single-step RL objective, where each context edit is rewarded by the improvement in downstream performance. We pair this objective with a tree-guided evolution loop. On Text-to-SQL generation (BIRD) and general question answering (MMLU-Redux), a 4B-parameter model trained with LSE outperforms self-evolving policies powered by GPT-5 and Claude Sonnet 4.5, as well as prompt optimization methods including GEPA and TextGrad, and transfers to guide other models without additional training. Our results highlight the effectiveness of treating self-evolution as a learnable skill.

Self-evolution is a central research topic in enabling large language model (LLM)-based agents to continually improve their capabilities after pretraining. Recent research has witnessed a transition from reinforcement learning (RL)-free to RL-based methods. Current RL-based methods either rely on dense external reward signals or extract intrinsic reward signals from LLMs themselves. However, these approaches diverge from the self-evolution mechanisms observed in human intelligence, where individuals learn and improve through mutual discussion and collaboration. In this work, we introduce Co-Evolving Multi-Agent Systems (CoMAS), a novel framework that enables agents to improve autonomously by learning from inter-agent interactions without external supervision. CoMAS generates intrinsic rewards from rich discussion dynamics, employs an LLM-as-a-judge mechanism to formulate these rewards, and optimizes each agent's policy through RL, thereby enabling decentralized and scalable co-evolution. Experimental results demonstrate that CoMAS consistently outperforms untrained agents and achieves state-of-the-art performance across most evaluation settings. Ablation studies confirm the necessity of interaction-based reward signals and reveal promising scalability as the number and diversity of agents increase. These findings establish CoMAS as a novel and effective paradigm for self-evolution in LLM-based agents.

We investigate the potential of large language models (LLMs) to serve as efficient simulators for agentic search tasks in reinforcement learning (RL), thereby reducing dependence on costly interactions with external search engines. To this end, we first quantify the intrinsic search capability of LLMs via structured prompting and repeated sampling, which we term Self-Search. Our results reveal that LLMs exhibit strong scaling behavior with respect to the inference budget, achieving high pass@k on question-answering benchmarks, including the challenging BrowseComp task. Building on these observations, we introduce Self-Search RL (SSRL), which enhances LLMs' Self-Search capability through format-based and rule-based rewards. SSRL enables models to iteratively refine their knowledge utilization internally, without requiring access to external tools. Empirical evaluations demonstrate that SSRL-trained policy models provide a cost-effective and stable environment for search-driven RL training, reducing reliance on external search engines and facilitating robust sim-to-real transfer. We draw the following conclusions: 1) LLMs possess world knowledge that can be effectively elicited to achieve high performance; 2) SSRL demonstrates the potential of leveraging internal knowledge to reduce hallucination; 3) SSRL-trained models integrate seamlessly with external search engines without additional effort. Our findings highlight the potential of LLMs to support more scalable RL agent training.

Reinforcement learning (RL) is an effective method of finding reasoning pathways in incomplete knowledge graphs (KGs). To overcome the challenges of a large action space, a self-supervised pre-training method is proposed to warm up the policy network before the RL training stage. To alleviate the distributional mismatch issue in general self-supervised RL (SSRL), in our supervised learning (SL) stage, the agent selects actions based on the policy network and learns from generated labels; this self-generation of labels is the intuition behind the name self-supervised. With this training framework, the information density of our SL objective is increased and the agent is prevented from getting stuck with the early rewarded paths. Our self-supervised RL (SSRL) method improves the performance of RL by pairing it with the wide coverage achieved by SL during pretraining, since the breadth of the SL objective makes it infeasible to train an agent with that alone. We show that our SSRL model meets or exceeds current state-of-the-art results on all Hits@k and mean reciprocal rank (MRR) metrics on four large benchmark KG datasets. This SSRL method can be used as a plug-in for any RL architecture for a KGR task. We adopt two RL architectures, i.e., MINERVA and MultiHopKG as our baseline RL models and experimentally show that our SSRL model consistently outperforms both baselines on all of these four KG reasoning tasks. Full code for the paper available at https://github.com/owenonline/Knowledge-Graph-Reasoning-with-Self-supervised-Reinforcement-Learning.

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT li2024chain,merrill2023expresssive.

We study self-rewarding reasoning large language models (LLMs), which can simultaneously generate step-by-step reasoning and evaluate the correctness of their outputs during the inference time-without external feedback. This integrated approach allows a single model to independently guide its reasoning process, offering computational advantages for model deployment. We particularly focus on the representative task of self-correction, where models autonomously detect errors in their responses, revise outputs, and decide when to terminate iterative refinement loops. To enable this, we propose a two-staged algorithmic framework for constructing self-rewarding reasoning models using only self-generated data. In the first stage, we employ sequential rejection sampling to synthesize long chain-of-thought trajectories that incorporate both self-rewarding and self-correction mechanisms. Fine-tuning models on these curated data allows them to learn the patterns of self-rewarding and self-correction. In the second stage, we further enhance the models' ability to assess response accuracy and refine outputs through reinforcement learning with rule-based signals. Experiments with Llama-3 and Qwen-2.5 demonstrate that our approach surpasses intrinsic self-correction capabilities and achieves performance comparable to systems that rely on external reward models.

Self-play, characterized by agents' interactions with copies or past versions of itself, has recently gained prominence in reinforcement learning. This paper first clarifies the preliminaries of self-play, including the multi-agent reinforcement learning framework and basic game theory concepts. Then it provides a unified framework and classifies existing self-play algorithms within this framework. Moreover, the paper bridges the gap between the algorithms and their practical implications by illustrating the role of self-play in different scenarios. Finally, the survey highlights open challenges and future research directions in self-play. This paper is an essential guide map for understanding the multifaceted landscape of self-play in RL.

Reinforcement learning from verifiable rewards (RLVR) has improved the reasoning abilities of LLMs, yet a fundamental limitation remains: models cannot learn from problems that are too difficult to solve under their current policy, as these yield no meaningful reward signal. We propose a simple yet effective solution based on task reformulation. We transform challenging open-ended problems into cognitively simpler variants -- such as multiple-choice and cloze formats -- that preserve the original answer while reducing the effective search space and providing denser learning signals. These reformulations span a spectrum from discriminative to generative tasks, which we exploit to bootstrap learning: models first learn from structured, easier formats, and this knowledge transfers back to improve performance on the original open-ended problems. Building on this insight, we introduce Cog-DRIFT, a framework that constructs reformulated variants and organizes them into an adaptive curriculum based on difficulty. Training progresses from easier to harder formats, enabling the model to learn from problems that previously yielded zero signal under standard RL post-training. Cog-DRIFT not only improves on the originally unsolvable hard problems (absolute +10.11% for Qwen and +8.64% for Llama) but also generalizes well to other held-out datasets. Across 2 models and 6 reasoning benchmarks, our method consistently outperforms standard GRPO and strong guided-exploration baselines. On average, Cog-DRIFT shows +4.72% (Qwen) and +3.23% (Llama) improvements over the second-best baseline. We further show that Cog-DRIFT improves pass@k at test time, and the curriculum improves sample efficiency. Overall, our results highlight task reformulation and curriculum learning as an effective paradigm for overcoming the exploration barrier in LLM post-training.

On-policy distillation (OPD) has become a popular training paradigm in the LLM community. This paradigm selects a larger model as the teacher to provide dense, fine-grained signals for each sampled trajectory, in contrast to reinforcement learning with verifiable rewards (RLVR), which only obtains sparse signals from verifiable outcomes in the environment. Recently, the community has explored on-policy self-distillation (OPSD), where the same model serves as both teacher and student, with the teacher receiving additional privileged information such as reference answers to enable self-evolution. This paper demonstrates that learning signals solely derived from the privileged teacher result in severe information leakage and unstable long-term training. Accordingly, we identify the optimal niche for self-distillation and propose RLSD (RLVR with Self-Distillation). Specifically, we leverage self-distillation to obtain token-level policy differences for determining fine-grained update magnitudes, while continuing to use RLVR to derive reliable update directions from environmental feedback (e.g., response correctness). This enables RLSD to simultaneously harness the strengths of both RLVR and OPSD, achieving a higher convergence ceiling and superior training stability.

Reinforcement learning (RL) promises a framework for near-universal problem-solving. In practice however, RL algorithms are often tailored to specific benchmarks, relying on carefully tuned hyperparameters and algorithmic choices. Recently, powerful model-based RL methods have shown impressive general results across benchmarks but come at the cost of increased complexity and slow run times, limiting their broader applicability. In this paper, we attempt to find a unifying model-free deep RL algorithm that can address a diverse class of domains and problem settings. To achieve this, we leverage model-based representations that approximately linearize the value function, taking advantage of the denser task objectives used by model-based RL while avoiding the costs associated with planning or simulated trajectories. We evaluate our algorithm, MR.Q, on a variety of common RL benchmarks with a single set of hyperparameters and show a competitive performance against domain-specific and general baselines, providing a concrete step towards building general-purpose model-free deep RL algorithms.

LLM-based web agents have recently made significant progress, but much of it has occurred in closed-source systems, widening the gap with open-source alternatives. Progress has been held back by two key challenges: first, a narrow focus on single-step tasks that overlooks the complexity of multi-step web interactions; and second, the high compute costs required to post-train LLM-based web agents. To address this, we present the first statistically grounded study on compute allocation for LLM web-agent post-training. Our approach uses a two-stage pipeline, training a Llama 3.1 8B student to imitate a Llama 3.3 70B teacher via supervised fine-tuning (SFT), followed by on-policy reinforcement learning. We find this process highly sensitive to hyperparameter choices, making exhaustive sweeps impractical. To spare others from expensive trial-and-error, we sample 1,370 configurations and use bootstrapping to estimate effective hyperparameters. Our results show that combining SFT with on-policy RL consistently outperforms either approach alone on both WorkArena and MiniWob++. Further, this strategy requires only 55% of the compute to match the peak performance of pure SFT on MiniWob++, effectively pushing the compute-performance Pareto frontier, and is the only strategy that can close the gap with closed-source models.

Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.

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.

Large language models (LLMs) have fueled many intelligent agent tasks, such as web navigation -- but most existing agents perform far from satisfying in real-world webpages due to three factors: (1) the versatility of actions on webpages, (2) HTML text exceeding model processing capacity, and (3) the complexity of decision-making due to the open-domain nature of web. In light of the challenge, we develop AutoWebGLM, a GPT-4-outperforming automated web navigation agent built upon ChatGLM3-6B. Inspired by human browsing patterns, we design an HTML simplification algorithm to represent webpages, preserving vital information succinctly. We employ a hybrid human-AI method to build web browsing data for curriculum training. Then, we bootstrap the model by reinforcement learning and rejection sampling to further facilitate webpage comprehension, browser operations, and efficient task decomposition by itself. For testing, we establish a bilingual benchmark -- AutoWebBench -- for real-world web browsing tasks. We evaluate AutoWebGLM across diverse web navigation benchmarks, revealing its improvements but also underlying challenges to tackle real environments. Related code, model, and data will be released at https://github.com/THUDM/AutoWebGLM.

Autonomous self-improving robots that interact and improve with experience are key to the real-world deployment of robotic systems. In this paper, we propose an online learning method, SELFI, that leverages online robot experience to rapidly fine-tune pre-trained control policies efficiently. SELFI applies online model-free reinforcement learning on top of offline model-based learning to bring out the best parts of both learning paradigms. Specifically, SELFI stabilizes the online learning process by incorporating the same model-based learning objective from offline pre-training into the Q-values learned with online model-free reinforcement learning. We evaluate SELFI in multiple real-world environments and report improvements in terms of collision avoidance, as well as more socially compliant behavior, measured by a human user study. SELFI enables us to quickly learn useful robotic behaviors with less human interventions such as pre-emptive behavior for the pedestrians, collision avoidance for small and transparent objects, and avoiding travel on uneven floor surfaces. We provide supplementary videos to demonstrate the performance of our fine-tuned policy on our project page.

Large language models (LLMs) have advanced rapidly in recent years, driven by scale, abundant high-quality training data, and reinforcement learning. Yet this progress faces a fundamental bottleneck: the need for ever more data from which models can continue to learn. In this work, we propose a reinforcement learning approach that removes this dependency by enabling models to improve without additional data. Our method leverages a game-theoretic framework of self-play, where a model's capabilities are cast as performance in a competitive game and stronger policies emerge by having the model play against itself - a process we call Language Self-Play (LSP). Experiments with Llama-3.2-3B-Instruct on instruction-following benchmarks show that pretrained models can not only enhance their performance on challenging tasks through self-play alone, but can also do so more effectively than data-driven baselines.

Video generative models trained on expert demonstrations have been utilized as performant text-conditioned visual planners for solving robotic tasks. However, generalization to unseen tasks remains a challenge. Whereas improved generalization may be facilitated by leveraging learned prior knowledge from additional pre-collected offline data sources, such as web-scale video datasets, in the era of experience we aim to design agents that can continuously improve in an online manner from self-collected behaviors. In this work we thus propose the Self-Adapting Improvement Loop (SAIL), where an in-domain video model iteratively updates itself on self-produced trajectories, collected through adaptation with an internet-scale pretrained video model, and steadily improves its performance for a specified task of interest. We apply SAIL to a diverse suite of MetaWorld tasks, as well as two manipulation tasks on a real robot arm, and find that performance improvements continuously emerge over multiple iterations for novel tasks initially unseen during original in-domain video model training. Furthermore, we discover that SAIL is surprisingly robust regarding if and how the self-collected experience is filtered, and the quality of the initial in-domain demonstrations. Through adaptation with summarized internet-scale data, and learning through online experience, we thus demonstrate a way to iteratively bootstrap a high-performance video model for solving novel robotic tasks through self-improvement.

Due to constraints on privacy, cost, and latency, on-premise deployment of small models is increasingly common. However, most practical pipelines stop at supervised fine-tuning (SFT) and fail to reach the reinforcement learning (RL) alignment stage. The main reason is that RL alignment typically requires either expensive human preference annotation or heavy reliance on high-quality reward models with large-scale API usage and ongoing engineering maintenance, both of which are ill-suited to on-premise settings. To bridge this gap, we propose a positive-unlabeled (PU) RL distillation method for on-premise small-model deployment. Without human-labeled preferences or a reward model, our method distills the teacher's preference-optimization capability from black-box generations into a locally trainable student. For each prompt, we query the teacher once to obtain an anchor response, locally sample multiple student candidates, and perform anchor-conditioned self-ranking to induce pairwise or listwise preferences, enabling a fully local training loop via direct preference optimization or group relative policy optimization. Theoretical analysis justifies that the induced preference signal by our method is order-consistent and concentrates on near-optimal candidates, supporting its stability for preference optimization. Experiments demonstrate that our method achieves consistently strong performance under a low-cost setting.

Truly reliable AI requires more than simply scaling up knowledge; it demands the ability to know what it knows and when it does not. Yet recent research shows that even the best LLMs misjudge their own competence in more than one in five cases, making any response born of such internal uncertainty impossible to fully trust. Inspired by self-improvement reinforcement learning techniques that require minimal data, we present a simple but powerful framework KnowRL that strengthens a model's internal understanding of its own feasibility boundaries, enabling safer and more responsible behaviour. Our framework combines two components: (i) introspection, where the model generates and classifies tasks it judges feasible or infeasible, and (ii) consensus-based rewarding, where stability of self-knowledge assessment is reinforced through internal agreement. By using internally generated data, this design strengthens consistency in self-knowledge and entirely avoids costly external supervision. In experiments on LLaMA-3.1-8B and Qwen-2.5-7B, KnowRL steadily improved self-knowledge, validated by both intrinsic self-consistency and extrinsic benchmarking. With nothing more than a small seed set and no external supervision, our method drove gains as high as 28% in accuracy and 12% in F1, outperforming baselines in just a few iterations. Our framework essentially unlocks the untapped capacity of LLMs to self-improve their knowledge awareness, opening the door to reliable, more accountable AI and safer deployment in critical applications. Owing to its simplicity and independence from external effort, we encourage applying this reliability-enhancing process to all future models.

Agentic reinforcement learning (RL) is emerging as a critical post-training paradigm for improving LLM agent capabilities. Existing RL algorithms for LLMs largely follow the token-centric paradigm as in RLHF and RLVR, where tokens serve as the basic units for modeling and optimization. However, this paradigm introduces a granularity mismatch in agentic RL, as it optimizes token-level predictions while LLM agents make step-level decisions through cycles of environmental observations and actions. To bridge this gap, we propose StepPO, a step-centric paradigm for agentic RL via step-aligned policy optimization. Specifically, we reformulate agentic RL from a token-level Markov Decision Process (MDP) into a step-level MDP, where interaction steps serve as the basic trajectory representations. We further propose step-level credit assignment to align policy optimization with the natural granularity of agent decisions. Together, StepPO optimizes agent policies at the step level for multi-turn agent-environment interaction. Experiments across multi-hop QA, academic paper search, and text-world action tasks show that StepPO consistently outperforms various RL algorithms. Further analyses provide insights into how step-centric paradigm improves agent training. We hope this step-centric paradigm offers a useful lens for understanding agent behavior and a practical path for training more capable LLM agents.

Reinforcement learning with verifiable rewards (RLVR) has become a core post-training recipe. Introducing suitable off-policy trajectories into on-policy exploration accelerates RLVR convergence and raises the performance ceiling, yet finding a source of such trajectories remains the key challenge. Existing mixed-policy methods either import trajectories from external teachers (high-quality but distributionally far) or replay past training trajectories (close but capped in quality), and neither simultaneously satisfies the strong enough (higher Q , more new knowledge to learn) and close enough (lower V , more readily absorbed) conditions required to maximize the effective learning signal S = Q/V. We propose Near-Future Policy Optimization (NPO), a simple mixed-policy scheme that learns from a policy's own near-future self: a later checkpoint from the same training run is a natural source of auxiliary trajectories that is both stronger than the current policy and closer than any external source, directly balancing trajectory quality against variance cost. We validate NPO through two manual interventions, early-stage bootstrapping and late-stage plateau breakthrough, and further propose AutoNPO,an adaptive variant that automatically triggers interventions from online training signals and selects the guide checkpoint that maximizes S. On Qwen3-VL-8B-Instruct with GRPO, NPO improves average performance from 57.88 to 62.84, and AutoNPO pushes it to 63.15, raising the final performance ceiling while accelerating convergence.

Scaling up self-supervised learning has driven breakthroughs in language and vision, yet comparable progress has remained elusive in reinforcement learning (RL). In this paper, we study building blocks for self-supervised RL that unlock substantial improvements in scalability, with network depth serving as a critical factor. Whereas most RL papers in recent years have relied on shallow architectures (around 2 - 5 layers), we demonstrate that increasing the depth up to 1024 layers can significantly boost performance. Our experiments are conducted in an unsupervised goal-conditioned setting, where no demonstrations or rewards are provided, so an agent must explore (from scratch) and learn how to maximize the likelihood of reaching commanded goals. Evaluated on simulated locomotion and manipulation tasks, our approach increases performance on the self-supervised contrastive RL algorithm by 2times - 50times, outperforming other goal-conditioned baselines. Increasing the model depth not only increases success rates but also qualitatively changes the behaviors learned. The project webpage and code can be found here: https://wang-kevin3290.github.io/scaling-crl/.

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.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for post-training reasoning models. However, group-based methods such as Group Relative Policy Optimization (GRPO) face a critical dilemma in sparse-reward settings: pure Reinforcement Learning (RL) suffers from advantage collapse and high-variance gradient estimation, while mixed-policy optimization introduces persistent distributional bias. To resolve this dilemma, we introduce Hindsight-Anchored Policy Optimization (HAPO). HAPO employs the Synthetic Success Injection (SSI) operator, a hindsight mechanism that selectively anchors optimization to teacher demonstrations during failure. This injection is governed by a Thompson sampling-inspired gating mechanism, creating an autonomous, self-paced curriculum. Theoretically, we demonstrate that HAPO achieves asymptotic consistency: by naturally annealing the teacher signal as the policy improves, HAPO recovers the unbiased on-policy gradient. This ensures off-policy guidance acts as a temporary scaffold rather than a persistent ceiling, enabling the model to surpass the limitations of static teacher forcing.

On-policy distillation (OPD), which leverages a pre-trained, specialized teacher model to provide dense supervisory signals, has achieved significant success in Large Language Models (LLMs) and has recently been adapted to flow matching models. However, this paradigm suffers from two major issues: First, training a separate, task-specific teacher for every new objective incurs high computational costs. Second, the discrepancy between teacher and student distributions often leads to compounding errors along the generation trajectory. In this paper, we introduce Self-OPD, a teacher-free OPD framework for flow matching models that turns the student's own self-exploration into step-wise supervision. At each timestep, Self-OPD branches the deterministic next-state prediction into K stochastic SDE candidates, rolls them out with the ODE sampler, and compares their rewards against a deterministic self-reference baseline to obtain normalized advantages. The velocity field is optimized with an all-branch pull-push objective, where high-advantage branches attract the student and low-advantage branches repel it under direction-aware attenuation and SDE-variance normalization. For multi-objective alignment, Self-OPD fuses normalized scores at the reward level, avoiding direct gradient conflict. Experiments on single and mixed reward benchmarks show that Self-OPD outperforms prior RL and OPD methods without task-specific teachers.

Self-play reinforcement learning has recently emerged as a way to train driving policies without any human data. It uses cheap, large-scale simulations to substitute expensive, large-scale human driving demonstrations. A key limitation of this approach is that policies trained through pure self-play can learn effective but alien driving conventions incompatible with people. Previous works attempt to mitigate such behavioral misalignments through extensive reward engineering and domain randomization, which are brittle and labor-intensive. Instead of completely discarding human demonstrations, our method treats them as a regularization objective on top of a minimal safe goal-reaching reward. Like the spice in a good stew, we find that a little human data goes a long way: our method uses only 30 minutes of human demonstrations, 2500x fewer than comparable imitation learning approaches. Resulting policies coordinate with held-out human trajectories and complete training in 15 hours on a single consumer-grade GPU. Videos and full source code are available at https://spiced-self-play.com/.

Reinforcement learning (RL) allows an agent interacting sequentially with an environment to maximize its long-term expected return. In the distributional RL (DistrRL) paradigm, the agent goes beyond the limit of the expected value, to capture the underlying probability distribution of the return across all time steps. The set of DistrRL algorithms has led to improved empirical performance. Nevertheless, the theory of DistrRL is still not fully understood, especially in the control case. In this paper, we present the simpler one-step distributional reinforcement learning (OS-DistrRL) framework encompassing only the randomness induced by the one-step dynamics of the environment. Contrary to DistrRL, we show that our approach comes with a unified theory for both policy evaluation and control. Indeed, we propose two OS-DistrRL algorithms for which we provide an almost sure convergence analysis. The proposed approach compares favorably with categorical DistrRL on various environments.

Self-evolving frameworks usually optimize task solutions while treating the surrounding harness as fixed. We introduce Harness-Aware Self-Evolving (HASE), an agentic reinforcement-learning framework in which a single model can generate task solutions or edit selected harness components in a multi-turn action space. HASE enables a single Qwen3-8B model to match the text-classification performance of a GPT-OSS-120B model that uses Claude Code as the harness proposer. In alpha factor mining, HASE outperforms the reported GPT-OSS-120B baseline. HASE also repairs imperfect evaluation components and converges to state-of-the-art performance in circle-packing algorithm discovery. These results show that HASE improves the harness and the solution through one unified agentic process.

Reinforcement learning is the method of choice to train models in sampling-based setups with binary outcome feedback, such as navigation, code generation, and mathematical problem solving. In such settings, models implicitly induce a likelihood over correct rollouts. However, we observe that reinforcement learning does not maximize this likelihood, and instead optimizes only a lower-order approximation. Inspired by this observation, we introduce Maximum Likelihood Reinforcement Learning (MaxRL), a sampling-based framework to approximate maximum likelihood using reinforcement learning techniques. MaxRL addresses the challenges of non-differentiable sampling by defining a compute-indexed family of sample-based objectives that interpolate between standard reinforcement learning and exact maximum likelihood as additional sampling compute is allocated. The resulting objectives admit a simple, unbiased policy-gradient estimator and converge to maximum likelihood optimization in the infinite-compute limit. Empirically, we show that MaxRL Pareto-dominates existing methods in all models and tasks we tested, achieving up to 20x test-time scaling efficiency gains compared to its GRPO-trained counterpart. We also observe MaxRL to scale better with additional data and compute. Our results suggest MaxRL is a promising framework for scaling RL training in correctness based settings.

Can a model learn to escape its own learning plateau? Reinforcement learning methods for finetuning large reasoning models stall on datasets with low initial success rates, and thus little training signal. We investigate a fundamental question: Can a pretrained LLM leverage latent knowledge to generate an automated curriculum for problems it cannot solve? To explore this, we design SOAR: A self-improvement framework designed to surface these pedagogical signals through meta-RL. A teacher copy of the model proposes synthetic problems for a student copy, and is rewarded with its improvement on a small subset of hard problems. Critically, SOAR grounds the curriculum in measured student progress rather than intrinsic proxy rewards. Our study on the hardest subsets of mathematical benchmarks (0/128 success) reveals three core findings. First, we show that it is possible to realize bi-level meta-RL that unlocks learning under sparse, binary rewards by sharpening a latent capacity of pretrained models to generate useful stepping stones. Second, grounded rewards outperform intrinsic reward schemes used in prior LLM self-play, reliably avoiding the instability and diversity collapse modes they typically exhibit. Third, analyzing the generated questions reveals that structural quality and well-posedness are more critical for learning progress than solution correctness. Our results suggest that the ability to generate useful stepping stones does not require the preexisting ability to actually solve the hard problems, paving a principled path to escape reasoning plateaus without additional curated data.

While current software agents powered by large language models (LLMs) and agentic reinforcement learning (RL) can boost programmer productivity, their training data (e.g., GitHub issues and pull requests) and environments (e.g., pass-to-pass and fail-to-pass tests) heavily depend on human knowledge or curation, posing a fundamental barrier to superintelligence. In this paper, we present Self-play SWE-RL (SSR), a first step toward training paradigms for superintelligent software agents. Our approach takes minimal data assumptions, only requiring access to sandboxed repositories with source code and installed dependencies, with no need for human-labeled issues or tests. Grounded in these real-world codebases, a single LLM agent is trained via reinforcement learning in a self-play setting to iteratively inject and repair software bugs of increasing complexity, with each bug formally specified by a test patch rather than a natural language issue description. On the SWE-bench Verified and SWE-Bench Pro benchmarks, SSR achieves notable self-improvement (+10.4 and +7.8 points, respectively) and consistently outperforms the human-data baseline over the entire training trajectory, despite being evaluated on natural language issues absent from self-play. Our results, albeit early, suggest a path where agents autonomously gather extensive learning experiences from real-world software repositories, ultimately enabling superintelligent systems that exceed human capabilities in understanding how systems are constructed, solving novel challenges, and autonomously creating new software from scratch.

On-policy self-distillation (OPSD) is a promising approach to improve reasoning language models, but it remains brittle in practice: making it work reliably often requires substantial engineering effort. We identify a structural source of this difficulty: vanilla OPSD is precisely the β=1 member of a broader policy-optimization family, where β weights the KL penalty anchoring the student to a reference policy. This equivalence turns β from an implicit value fixed at one into a controllable regularization parameter, yielding a more general formulation that trades off proximity to a reference policy against privileged teacher guidance. We introduce β-OPSD and derive its optimal policy as a geometric interpolation between the reference policy and the privileged teacher. Directly optimizing this objective with reinforcement learning, however, would be costly and high-variance. Rather than optimize the RL objective directly, we turn its closed-form solution into a distillation target. Each value of β selects a target along the reference-to-teacher path, which we implement efficiently by mixing their token-level logits. In this way, inexpensive distillation approximates the solution of expensive policy optimization. Return-to-go credit assignment further aligns token updates with the sequence-level objective while retaining the simplicity of OPSD. Experiments on mathematical reasoning benchmarks show that β-OPSD consistently outperforms vanilla OPSD, improving optimization stability and downstream reasoning performance. Our results provide a principled route from self-distillation to policy optimization and back without sacrificing the efficiency that makes OPSD practical.

Recently, large reasoning models demonstrate exceptional performance on various tasks. However, reasoning models inefficiently over-process both trivial and complex queries, leading to resource waste and prolonged user latency. To address this challenge, we propose SelfBudgeter - a self-adaptive controllable reasoning strategy for efficient reasoning. Our approach adopts a dual-phase training paradigm: first, the model learns to pre-estimate the reasoning cost based on the difficulty of the query. Then, we introduce budget-guided GPRO for reinforcement learning, which effectively maintains accuracy while reducing output length. SelfBudgeter allows users to anticipate generation time and make informed decisions about continuing or interrupting the process. Furthermore, our method enables direct manipulation of reasoning length via pre-filling token budget. Experimental results demonstrate that SelfBudgeter can rationally allocate budgets according to problem complexity, achieving up to 74.47% response length compression on the MATH benchmark while maintaining nearly undiminished accuracy.

Agent harness evolution improves frozen language-model agents by modifying the executable structures around them. We study this paradigm as a form of sample-efficient fast adaptation: instead of updating model weights, an agent can acquire task-specific competence by changing its external harness, while leaving the base model's general capabilities intact. Prior work shows that self-generated rollouts can support harness search, suggesting that agents may acquire new task competence through practice. Yet in long-horizon stochastic environments, self-practice becomes fragile: rewards are sparse, outcomes are high-variance, and failures are hard to attribute to concrete harness mechanisms. We introduce DemoEvolve, a demonstration-bootstrapped approach to harness evolution. When reward-only search is too broad and noisy, competent human trajectories serve as expert reference experience for the coding proposer, guiding harness-level diagnosis and editing. Experiments on Liar's Dice show that self-rollout evolution can work when episodes are short and failures are attributable. In contrast, Balatro exposes a harder long-horizon stochastic regime, where self-rollout evolution is misled by sparse feedback and candidate-selection noise, while tutorial-like textual knowledge alone does not yield stable improvement. Under the same limited budget, DemoEvolve produces more effective and auditable harness edits and achieves better performance. Overall, demonstrations make sparse-feedback harness evolution more diagnosable, localizable, and stable.

Continuous self-improvement requires an ever-expanding pool of self-generated, diverse, adaptive goals. For language agents, existing training environment pools (hand-curated, statically synthesized, or frozen-verifier) keep the goal distribution fixed as the learner scales. We introduce SPADE (Self-Play in Adaptive Synthetic Executable Environments), a self-play RL framework in which a single LLM plays two roles: an Environment Designer that writes complete, long-horizon training environments as executable code with an OpenAI Gym-style reset()/step() interface, and a Reasoning Agent that learns to act in them. Each is a stateful, multi-turn environment (state transitions, reward functions, and verification code), so one interface spans reasoning problems and multi-step agentic tool use. The Reasoning Agent's regret is estimated using the gap between its reward with and without privileged hints; in optimizing this regret signal the Environment Designer learns to target environments at the edge of the agent's capabilities while keeping them feasible. Through extensive experimentation, we find several components critical to success: grounding the Environment Designer on documents sampled from a large pretraining corpus, and giving it an accumulated environment memory. Scaling to 30B-parameter models, SPADE improves over the strongest fixed-environment baseline by +5.3 on average across eight held-out math, science, code, and reasoning benchmarks, and lifts the tool-use setting by +5.7 on BFCL-v4 multi-turn and +13.9 on ACEBench-Agent; on the games setting, the margin over the strongest baseline grows with model scale. By making environment design itself a learnable component, SPADE takes a concrete step toward open-ended self-improvement.

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.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but suffers from advantage collapse on ``hard samples'' where all rollouts fail. This lack of variance eliminates crucial learning signals. For these intractable samples, simply scaling up rollout budgets offers limited gains. We introduce Joint Policy and Prompt Optimization (P^2O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P^2O leverages the GEPA algorithm to discover successful reasoning prompts for intractable instances. Via context distillation, the model internalizes these prompt-induced gains directly into its parameters, removing the need for inference-time prompting. Empirically, P^2O restores critical advantage signals, significantly outperforming standard GRPO and surpassing baselines with doubled rollout budgets, ultimately yielding strong out-of-distribution generalization and an up to 9.5% performance improvement. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates establishes a self-reinforcing paradigm for autonomous LLM alignment.

Search-augmented reasoning agents interleave internal reasoning with calls to an external retriever, and their performance relies on the quality of each issued query. However, under outcome-reward reinforcement learning, every search decision in a rollout shares the same trajectory-level reward, leaving individual queries without step-specific credit. Recent process-supervision approaches address this gap by drawing step-level signals from outside the policy, relying either on a much larger teacher model, or on sub-question annotations produced by a stronger external system. In contrast, we propose SD-Search, which derives step-level supervision from the policy itself through on-policy hindsight self-distillation, requiring neither an external teacher nor additional annotations. In SD-Search, a single model plays two roles that differ only in conditioning: a student that sees only the context available at inference time, and a teacher that additionally conditions on a compact hindsight block summarizing the search queries and final outcomes of a group of rollouts sampled from the same question. Since the teacher knows how each rollout unfolded and which ones succeeded, its query distribution implicitly marks which decisions were worth making, and the student is trained to recover this behavior by minimizing the token-level Jensen--Shannon divergence to the teacher at search-query positions. This layers a dense, step-level signal on top of GRPO's coarse trajectory reward. Crucially, this signal is produced by the policy itself within the standard RL training loop, without external model inference, auxiliary annotation pipeline, or additional training stage.

While Large Language Models (LLMs) excel in language-based agentic tasks, their applicability to unseen, nonlinguistic environments (e.g., symbolic or spatial tasks) remains limited. Previous work attributes this performance gap to the mismatch between the pretraining distribution and the testing distribution. In this work, we demonstrate the primary bottleneck is the prohibitive cost of exploration: mastering these tasks requires extensive trial-and-error, which is computationally unsustainable for parameter-heavy LLMs operating in a high dimensional semantic space. To address this, we propose SCOUT (Sub-Scale Collaboration On Unseen Tasks), a novel framework that decouples exploration from exploitation. We employ lightweight "scouts" (e.g., small MLPs) to probe environmental dynamics at a speed and scale far exceeding LLMs. The collected trajectories are utilized to bootstrap the LLM via Supervised Fine-Tuning (SFT), followed by multi-turn Reinforcement Learning (RL) to activate its latent world knowledge. Empirically, SCOUT enables a Qwen2.5-3B-Instruct model to achieve an average score of 0.86, significantly outperforming proprietary models, including Gemini-2.5-Pro (0.60), while saving about 60% GPU hours consumption.

We study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson line in 4D {cal N}=4 super-Yang-Mills theory. We introduce an improved truncation scheme with an 'OPE tail' approximation and use it to reproduce the 'bootstrability' results of Cavagli\`a et al. for the OPE-coefficients squared of the first three unprotected operators. For example, for the first OPE-coefficient squared at 't Hooft coupling (4pi)^2, linear-functional methods with two sum rules from integrated correlators give the rigorous result 0.294014873 pm 4.88 cdot 10^{-8}, whereas our methods give with machine-precision computations 0.294014228 pm 6.77 cdot 10^{-7}. For our numerical searches, we benchmark the Reinforcement Learning Soft Actor-Critic algorithm against an Interior Point Method algorithm (IPOPT) and comment on the merits of each algorithm.

Large language models are increasingly post-trained with reinforcement learning in verifiable domains such as code and math. Yet, current methods for reinforcement learning with verifiable rewards (RLVR) learn only from a scalar outcome reward per attempt, creating a severe credit-assignment bottleneck. Many verifiable environments actually provide rich textual feedback, such as runtime errors or judge evaluations, that explain why an attempt failed. We formalize this setting as reinforcement learning with rich feedback and introduce Self-Distillation Policy Optimization (SDPO), which converts tokenized feedback into a dense learning signal without any external teacher or explicit reward model. SDPO treats the current model conditioned on feedback as a self-teacher and distills its feedback-informed next-token predictions back into the policy. In this way, SDPO leverages the model's ability to retrospectively identify its own mistakes in-context. Across scientific reasoning, tool use, and competitive programming on LiveCodeBench v6, SDPO improves sample efficiency and final accuracy over strong RLVR baselines. Notably, SDPO also outperforms baselines in standard RLVR environments that only return scalar feedback by using successful rollouts as implicit feedback for failed attempts. Finally, applying SDPO to individual questions at test time accelerates discovery on difficult binary-reward tasks, achieving the same discovery probability as best-of-k sampling or multi-turn conversations with 3x fewer attempts.

Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory, which is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5 percent overhead per step from a single additional forward pass.

Self-supervised learning of convolutional neural networks can harness large amounts of cheap unlabeled data to train powerful feature representations. As surrogate task, we jointly address ordering of visual data in the spatial and temporal domain. The permutations of training samples, which are at the core of self-supervision by ordering, have so far been sampled randomly from a fixed preselected set. Based on deep reinforcement learning we propose a sampling policy that adapts to the state of the network, which is being trained. Therefore, new permutations are sampled according to their expected utility for updating the convolutional feature representation. Experimental evaluation on unsupervised and transfer learning tasks demonstrates competitive performance on standard benchmarks for image and video classification and nearest neighbor retrieval.

Self-improving systems require environmental interaction for continuous adaptation. We introduce SPICE (Self-Play In Corpus Environments), a reinforcement learning framework where a single model acts in two roles: a Challenger that mines documents from a large corpus to generate diverse reasoning tasks, and a Reasoner that solves them. Through adversarial dynamics, the Challenger creates an automatic curriculum at the frontier of the Reasoner's capability, while corpus grounding provides the rich, near-inexhaustible external signal necessary for sustained improvement. Unlike existing ungrounded self-play methods that offer more limited benefits, SPICE achieves consistent gains across mathematical (+8.9%) and general reasoning (+9.8%) benchmarks on multiple model families. Our analysis reveals how document grounding is a key ingredient in SPICE to continuously generate its own increasingly challenging goals and achieve them, enabling sustained self-improvement.

Self-play bootstraps LLM reasoning through an iterative Challenger-Solver loop: the Challenger is trained to generate questions that target the Solver's capabilities, and the Solver is optimized on the generated data to expand its reasoning skills. However, existing frameworks like R-Zero often exhibit non-sustained improvement, where early gains degrade as self-play continues. We identify a key failure mode, Diversity Illusion, where the Solver's training signals appear diverse yet collapse into recurring underlying patterns. It manifests as (1) Local Diversity Illusion, where diversity is enforced only within-batch, inducing cross-iteration mode cycling; and (2) Surface Diversity Illusion, where questions vary superficially but require near-identical reasoning skills. To mitigate them, we propose R-Diverse with two aligned innovations: Memory-Augmented Penalty (MAP), which uses a persistent memory bank to discourage recycling across iterations, and Skill-Aware Measurement (SAM), which evaluates diversity by the reasoning skills exercised rather than surface variation of questions. Across 10 math and general reasoning benchmarks, R-Diverse sustains gains over more iterations and consistently outperforms prior self-play methods. Code is available at https://github.com/Gengsheng-Li/R-Diverse.

For multi-agent reinforcement learning systems (MARLS), the problem formulation generally involves investing massive reward engineering effort specific to a given problem. However, this effort often cannot be translated to other problems; worse, it gets wasted when system dynamics change drastically. This problem is further exacerbated in sparse reward scenarios, where a meaningful heuristic can assist in the policy convergence task. We propose GOVerned Reward Engineering Kernels (GOV-REK), which dynamically assign reward distributions to agents in MARLS during its learning stage. We also introduce governance kernels, which exploit the underlying structure in either state or joint action space for assigning meaningful agent reward distributions. During the agent learning stage, it iteratively explores different reward distribution configurations with a Hyperband-like algorithm to learn ideal agent reward models in a problem-agnostic manner. Our experiments demonstrate that our meaningful reward priors robustly jumpstart the learning process for effectively learning different MARL problems.

On-policy reinforcement learning (RL) has become a popular framework for solving sequential decision problems due to its computational efficiency and theoretical simplicity. Some on-policy methods guarantee every policy update is constrained to a trust region relative to the prior policy to ensure training stability. These methods often require computationally intensive non-linear optimization or require a particular form of action distribution. In this work, we show that applying KL penalization alone is nearly sufficient to enforce such trust regions. Then, we show that introducing a "fixup" phase is sufficient to guarantee a trust region is enforced on every policy update while adding fewer than 5% additional gradient steps in practice. The resulting algorithm, which we call FixPO, is able to train a variety of policy architectures and action spaces, is easy to implement, and produces results competitive with other trust region methods.

While reinforcement learning (RL) has achieved great success in acquiring complex skills solely from environmental interactions, it assumes that resets to the initial state are readily available at the end of each episode. Such an assumption hinders the autonomous learning of embodied agents due to the time-consuming and cumbersome workarounds for resetting in the physical world. Hence, there has been a growing interest in autonomous RL (ARL) methods that are capable of learning from non-episodic interactions. However, existing works on ARL are limited by their reliance on prior data and are unable to learn in environments where task-relevant interactions are sparse. In contrast, we propose a demonstration-free ARL algorithm via Implicit and Bi-directional Curriculum (IBC). With an auxiliary agent that is conditionally activated upon learning progress and a bidirectional goal curriculum based on optimal transport, our method outperforms previous methods, even the ones that leverage demonstrations.

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

Graphical User Interface (GUI) agents have made substantial strides in understanding and executing user instructions across diverse platforms. Yet, grounding these instructions to precise interface elements remains challenging, especially in complex, high-resolution, professional environments. Traditional supervised finetuning (SFT) methods often require large volumes of diverse data and exhibit weak generalization. To overcome these limitations, we introduce a reinforcement learning (RL) based framework that incorporates three core strategies: (1) seed data curation to ensure high quality training samples, (2) a dense policy gradient that provides continuous feedback based on prediction accuracy, and (3) a self evolutionary reinforcement finetuning mechanism that iteratively refines the model using attention maps. With only 3k training samples, our 7B-parameter model achieves state-of-the-art results among similarly sized models on three grounding benchmarks. Notably, it attains 47.3\% accuracy on the ScreenSpot-Pro dataset, outperforming much larger models, such as UI-TARS-72B, by a margin of 24.2\%. These findings underscore the effectiveness of RL-based approaches in enhancing GUI agent performance, particularly in high-resolution, complex environments.

Reinforcement learning (RL) theory has largely focused on proving minimax sample complexity bounds. These require strategic exploration algorithms that use relatively limited function classes for representing the policy or value function. Our goal is to explain why deep RL algorithms often perform well in practice, despite using random exploration and much more expressive function classes like neural networks. Our work arrives at an explanation by showing that many stochastic MDPs can be solved by performing only a few steps of value iteration on the random policy's Q function and then acting greedily. When this is true, we find that it is possible to separate the exploration and learning components of RL, making it much easier to analyze. We introduce a new RL algorithm, SQIRL, that iteratively learns a near-optimal policy by exploring randomly to collect rollouts and then performing a limited number of steps of fitted-Q iteration over those rollouts. Any regression algorithm that satisfies basic in-distribution generalization properties can be used in SQIRL to efficiently solve common MDPs. This can explain why deep RL works, since it is empirically established that neural networks generalize well in-distribution. Furthermore, SQIRL explains why random exploration works well in practice. We leverage SQIRL to derive instance-dependent sample complexity bounds for RL that are exponential only in an "effective horizon" of lookahead and on the complexity of the class used for function approximation. Empirically, we also find that SQIRL performance strongly correlates with PPO and DQN performance in a variety of stochastic environments, supporting that our theoretical analysis is predictive of practical performance. Our code and data are available at https://github.com/cassidylaidlaw/effective-horizon.

Exploration in sparse reward environments remains one of the key challenges of model-free reinforcement learning. Instead of solely relying on extrinsic rewards provided by the environment, many state-of-the-art methods use intrinsic rewards to encourage exploration. However, we show that existing methods fall short in procedurally-generated environments where an agent is unlikely to visit a state more than once. We propose a novel type of intrinsic reward which encourages the agent to take actions that lead to significant changes in its learned state representation. We evaluate our method on multiple challenging procedurally-generated tasks in MiniGrid, as well as on tasks with high-dimensional observations used in prior work. Our experiments demonstrate that this approach is more sample efficient than existing exploration methods, particularly for procedurally-generated MiniGrid environments. Furthermore, we analyze the learned behavior as well as the intrinsic reward received by our agent. In contrast to previous approaches, our intrinsic reward does not diminish during the course of training and it rewards the agent substantially more for interacting with objects that it can control.

Self-evolving agents violate the assumption behind most learning-theoretic guarantees: the data, evaluator, components, and hypothesis space are produced by the policy being updated. We present SEA, an architecture that confines self-modification to a small steering adapter and a versioned harness around a frozen base model and admits each modification only through an anytime-valid gate that emits an auditable certificate against a fixed error budget. Five loop controllers compose published guarantees; because such gates can only select among behaviors the frozen base already produces, five verifier-in-the-loop mechanisms -- best-of-N, micro-step search, self-authored reproduction oracles, search-layer control, and self-repair -- supply the dense, grader-free signal the gates require, computed from the issue text alone. On a 52-instance SWE-bench Verified subset across four base models, base capability is the dominant, confound-free effect, and on two strong base models a deliberate no-op-composite control isolates the suite's contribution at +4 and +5 (Glm~5.2 24to28; Gpt 29to34, the 65% best), with event logs confirming that its mechanisms fire and prevent regressions. Results are single-run on expensive evaluations; confirming run-to-run variance and adapting the per-task algorithm mix are future work.

Large-scale high-quality training data is important for improving the performance of models. After trained with data that has rationales (reasoning steps), models gain reasoning capability. However, the dataset with high-quality rationales is relatively scarce due to the high annotation cost. To address this issue, we propose Self-motivated Learning framework. The framework motivates the model itself to automatically generate rationales on existing datasets. Based on the inherent rank from correctness across multiple rationales, the model learns to generate better rationales, leading to higher reasoning capability. Specifically, we train a reward model with the rank to evaluate the quality of rationales, and improve the performance of reasoning through reinforcement learning. Experiment results of Llama2 7B on multiple reasoning datasets show that our method significantly improves the reasoning ability of models, even outperforming text-davinci-002 in some datasets.

The application of Reinforcement Learning (RL) in real world environments can be expensive or risky due to sub-optimal policies during training. In Offline RL, this problem is avoided since interactions with an environment are prohibited. Policies are learned from a given dataset, which solely determines their performance. Despite this fact, how dataset characteristics influence Offline RL algorithms is still hardly investigated. The dataset characteristics are determined by the behavioral policy that samples this dataset. Therefore, we define characteristics of behavioral policies as exploratory for yielding high expected information in their interaction with the Markov Decision Process (MDP) and as exploitative for having high expected return. We implement two corresponding empirical measures for the datasets sampled by the behavioral policy in deterministic MDPs. The first empirical measure SACo is defined by the normalized unique state-action pairs and captures exploration. The second empirical measure TQ is defined by the normalized average trajectory return and captures exploitation. Empirical evaluations show the effectiveness of TQ and SACo. In large-scale experiments using our proposed measures, we show that the unconstrained off-policy Deep Q-Network family requires datasets with high SACo to find a good policy. Furthermore, experiments show that policy constraint algorithms perform well on datasets with high TQ and SACo. Finally, the experiments show, that purely dataset-constrained Behavioral Cloning performs competitively to the best Offline RL algorithms for datasets with high TQ.

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it requires explicit reward functions that are often unavailable. Learning from expert demonstrations, the primary alternative, is dominated by supervised fine-tuning (SFT), which is inherently off-policy. We introduce Self-Distillation Fine-Tuning (SDFT), a simple method that enables on-policy learning directly from demonstrations. SDFT leverages in-context learning by using a demonstration-conditioned model as its own teacher, generating on-policy training signals that preserve prior capabilities while acquiring new skills. Across skill learning and knowledge acquisition tasks, SDFT consistently outperforms SFT, achieving higher new-task accuracy while substantially reducing catastrophic forgetting. In sequential learning experiments, SDFT enables a single model to accumulate multiple skills over time without performance regression, establishing on-policy distillation as a practical path to continual learning from demonstrations.

While large language models (LLMs) have demonstrated strong performance on complex reasoning tasks such as competitive programming (CP), existing methods predominantly focus on single-attempt settings, overlooking their capacity for iterative refinement. In this paper, we present RefineRL, a novel approach designed to unleash the self-refinement capabilities of LLMs for CP problem solving. RefineRL introduces two key innovations: (1) Skeptical-Agent, an iterative self-refinement agent equipped with local execution tools to validate generated solutions against public test cases of CP problems. This agent always maintains a skeptical attitude towards its own outputs and thereby enforces rigorous self-refinement even when validation suggests correctness. (2) A reinforcement learning (RL) solution to incentivize LLMs to self-refine with only standard RLVR data (i.e., problems paired with their verifiable answers). Extensive experiments on Qwen3-4B and Qwen3-4B-2507 demonstrate that our method yields substantial gains: after our RL training, these compact 4B models integrated with the Skeptical-Agent not only outperform much larger 32B models but also approach the single-attempt performance of 235B models. These findings suggest that self-refinement holds considerable promise for scaling LLM reasoning, with significant potential for further advancement.

The emergence of agentic reinforcement learning (Agentic RL) marks a paradigm shift from conventional reinforcement learning applied to large language models (LLM RL), reframing LLMs from passive sequence generators into autonomous, decision-making agents embedded in complex, dynamic worlds. This survey formalizes this conceptual shift by contrasting the degenerate single-step Markov Decision Processes (MDPs) of LLM-RL with the temporally extended, partially observable Markov decision processes (POMDPs) that define Agentic RL. Building on this foundation, we propose a comprehensive twofold taxonomy: one organized around core agentic capabilities, including planning, tool use, memory, reasoning, self-improvement, and perception, and the other around their applications across diverse task domains. Central to our thesis is that reinforcement learning serves as the critical mechanism for transforming these capabilities from static, heuristic modules into adaptive, robust agentic behavior. To support and accelerate future research, we consolidate the landscape of open-source environments, benchmarks, and frameworks into a practical compendium. By synthesizing over five hundred recent works, this survey charts the contours of this rapidly evolving field and highlights the opportunities and challenges that will shape the development of scalable, general-purpose AI agents.

Reinforcement learning with verifiable rewards (RLVR) efficiently scales the reasoning ability of large language models (LLMs) but is bottlenecked by scarce labeled data. Reinforcement learning with intrinsic rewards (RLIR) offers a scalable alternative via self-rewarding, yet often suffers from instability and inferior performance. We trace this gap to a systemic bias in confidence-coupled self-rewarding: the model tends to over-reward high-confidence mistakes, forming a self-confirming loop. We quantify this feedback-loop bias with three metrics: reward noise magnitude (rho_noise), policy-reward coupling (rho_selfbias), and over-/under-reward skew (rho_symbias). Our analyses show a compounding effect where strong coupling amplifies confidence-conditioned errors and drives a drift toward over-reward, leading to instability and a lower performance ceiling. To mitigate this, we propose reinforcement learning with ensembled rewards (RLER), which aggregates diverse models with adaptive reward interpolation and disagreement-aware rollout selection to reduce coupling and suppress over-reward drift. Extensive experiments show that RLER improves by 6.2% over the best RLIR baseline and is within 3.6% of RLVR, while exhibiting stable scaling on unlabeled samples.