Daily Papers

Converting verifier outcomes into useful policy updates and partial progress into complete task resolution is crucial for terminal agents. We present Terminal-RSI, which alternates Recursive Self-Rewrite (RSR) of verified trajectories with critic-inheriting Recursive Policy-Refine (RPR). We formulate Turn-Boundary Skip-Observation GAE (TB-GAE) to retain token-specific baselines while applying decay across interaction turns. Family Dense Reward (FDR) calibrates semantic progress across task families; Success-Prioritized Reward (SPR) separates strict success from bounded partial credit. A Warm-up Critic Model, recursive critic handoff, and stage-specific learning rates coordinate the two refinement phases. The five-stage sequence from Qwen3.8-27B base model through RSR-1, RPR-1, RSR-2, and RPR-2 yields Terminal-RSI-27B: 19.84% on Terminal-Bench 4.0, 86.52% on Terminal-Bench 2.1, 16.95% on Terminal-Bench 3.0, and 79.00% on Terminal-Bench Hard. On LHTB, process reward rises from 0.21 to 0.37 and strict completion from 0/46 to 5/46; SWR100 success doubles from 3.00% to 6.00%. By recursively coupling verified trajectory rewriting with critic-inheriting policy refinement, each retained stage consolidates discovered behaviors and progressively advances the agent from partial local repairs to strict terminal verification.

AI systems increasingly participate in their own improvement: revising their outputs, adapting their own harnesses during deployment, training on data they generate, and, increasingly, conducting AI research itself. This literature is described under a vocabulary ("self-refine," "self-reward," "self-play," "self-evolve") that conflates fundamentally different ambitions. We survey 1,250 arXiv papers (2024-2026) along two axes: what the system improves -- its behavior in deployment, its policy through training, its evaluator, or the research process itself -- and the degree of loop closure (human-in-the-loop to fully closed). The taxonomy separates bounded self-refinement -- convergent, evaluable, and already industrial practice -- from open-ended recursive self-improvement (RSI), which remains bounded by grounding requirements, collapse dynamics, and compute constraints on every measured axis. Its distinctive feature is a dedicated category for self-evaluation: every improvement loop is a claim that some signal can substitute for human judgment. We survey the evaluator design space -- judges, process reward models, verifiers, rubrics, meta-evaluation -- order the signals into a verification hierarchy from formal verifiers (strongest) to intrinsic self-assessment (weakest), and observe that demonstrated self-improvement strength tracks this hierarchy, that its failure modes (self-confirming loops, model collapse, diversity collapse) follow from its violations, and that the "research direction-setting" bottleneck keeping humans in the loop sits at the top of that hierarchy. We connect the technical literature to the theory of RSI limits and to the safety and governance questions raised by frontier-lab accounts of closing the loop, and identify governance-grade measurement of self-improvement as the field's most underpopulated niche.

On-policy distillation (OPD) provides dense, per-token supervision for language model post-training, but its effectiveness is bottlenecked by teacher quality: external teachers suffer from distribution mismatch, while self-distillation with privileged conditioning is limited by in-context learning capacity. We propose RISE (Recursive Improvement via Self-Extrapolating Policy Distillation), which constructs a synthetic teacher directly from the model's own RLVR training trajectory. By extrapolating the displacement between the current checkpoint and a trailing anchor---in parameter space or output logit space---RISE converts a sparse outcome-induced parameter update into a dense token-level target, without any external model or privileged conditioning. RISE combines RLVR and OPD in a complementary loop: outcome rewards ground the extrapolation toward correct reasoning, while the extrapolated teacher refines token-level decisions. Moreover, since the teacher is refreshed every iteration as the student improves, distillation becomes a recursive improvement mechanism rather than a one-shot compression step. Experiments spanning mathematical reasoning, multi-domain STEM, code generation, and multi-turn agentic tasks show that RISE outperforms RLVR-only training and on-policy self-distillation across all settings.

Recursive self-improvement is becoming increasingly vital for autonomous AI agents, where progress hinges on discovering high-value solutions across complex domains. The driver of this process is effective exploration, however, managing and improving exploration strategies remains a major bottleneck. Current systems face a fundamental dilemma: fixed strategies fail to adapt as search spaces scale, while online policy optimization requires navigating vast meta-search spaces under delayed and expensive feedback over long-horizon rollouts. We introduce Dream-RSI, a framework for scalable and recursively self-improving exploration. A lightweight orchestration layer makes exploration explicit and programmable while leaving the underlying coding agent unchanged. Our key insight is that accumulated discovery history can serve as a replay simulator over the realized search space. By performing dreaming in the replay simulator constructed from historical discovery trees, Dream-RSI secures immediate, low-cost off-policy feedback to evaluate and refine exploration policies without invoking repetitive, expensive online evaluations. The improved policy is subsequently redeployed online to drive further discovery, continuously expanding the simulator pool in a self-improving loop. Across algorithm engineering, mathematical optimization, and GPU kernel engineering, Dream-RSI achieves competitive or improved discovery quality while substantially reducing discovery cost in several settings.

Iterative refinement has been a promising paradigm to enable large language models (LLMs) to resolve difficult reasoning and problem-solving tasks. One of the key challenges, however, is how to effectively search through the enormous search space of possible refinements. Existing methods typically fall back on predefined heuristics, which are troubled by the exploration-exploitation dilemma and cannot adapt based on past refinement outcomes. We introduce Tree-Guided Policy Refinement (TGPR), a novel framework that combines GRPO with a Thompson-Sampling-based tree search. TGPR explores both failed and successful refinement paths actively, with denser training trajectories and more adaptive policies. On HumanEval, MBPP, and APPS benchmarks, our method achieves up to +4.2 percentage points absolute improvement in pass@1 (on MBPP) and up to +12.51 percentage points absolute improvement in pass@10 (on APPS) compared to a competitive GRPO baseline. Apart from debugging code, TGPR focuses on a principled approach to combining learned policies with structured search methods, offering a general framework for enhancing iterative refinement and stateful reasoning in LLMs.

Reinforcement Learning from Human Feedback (RLHF) has been commonly used to align the behaviors of Large Language Models (LLMs) with human preferences. Recently, a popular alternative is Direct Policy Optimization (DPO), which replaces an LLM-based reward model with the policy itself, thus obviating the need for extra memory and training time to learn the reward model. However, DPO does not consider the relative qualities of the positive and negative responses, and can lead to sub-optimal training outcomes. To alleviate this problem, we investigate the use of intrinsic knowledge within the on-the-fly fine-tuning LLM to obtain relative qualities and help to refine the loss function. Specifically, we leverage the knowledge of the LLM to design a refinement function to estimate the quality of both the positive and negative responses. We show that the constructed refinement function can help self-refine the loss function under mild assumptions. The refinement function is integrated into DPO and its variant Identity Policy Optimization (IPO). Experiments across various evaluators indicate that they can improve the performance of the fine-tuned models over DPO and IPO.

Code-as-Policy agents accomplish long-horizon embodied tasks by generating and executing code, yet continually improving them with teachers that are stronger but not globally reliable remains a key challenge. Existing distillation methods typically treat the teacher's complete behavior as the supervision target and thus misassign training credit on states where the teacher fails. We propose RE-0, a recursively verified policy improvement framework: rather than assuming that the teacher globally outperforms the student, RE-0 requests local corrections from the teacher on the student's own failure histories and checks in the environment whether each correction is genuinely beneficial; verified corrections yield immediate improvement. Building on this, we propose RE-OPD, which turns verified interventions into supervision for on-policy distillation. Only counterfactually verified teacher interventions provide distribution-level supervision, weighted by their measured local benefit, and the improvement they induce is projected back into the standalone student, so both where supervision is applied and how much credit the teacher receives co-evolve with the student policy. We further prove that the student's per-round gain is lower-bounded by its verified intervention gain up to verification and projection error terms. Experiments across multiple Code-as-Policy embodied tasks show that RE-0 improves both teacher-assisted execution and the standalone student, and generalizes to novel robots and scenes.

An agent can improve its behavior within an unresolved problem by changing how it acts and which experience it retains. We propose MMLA-RSI, a recursive self-improvement scheme with two implementations in Memory-Mediated Learning Architecture: Reasoning-Time Training (RTT) changes the policy state Φ, while Reasoning-Time Memory Adaptation (RTMA) changes authoritative memory M. Each route also makes its adaptation method an object of improvement. A current numerical updater trains the policy proposing its successor; a current memory manager chooses the records available to the process proposing its successor. An independently admitted successor takes over the same role in the next generation. We give bounded executable rule languages, shared task/proposal interfaces, and one algorithm for either route or their composition. The RTT instance changes scalar schedules in a clipped-momentum update. The RTMA instance chooses NULL or a complete-row write with possible eviction. A fixed interpreter, trusted committer, and independent evaluator bound what can change. State versions, read closures, and conditional properties describe causal execution, accepted transitions, and finite work. Existing numerical-component studies motivate the construction. In four-candidate program selection, retaining LARC feedback updates reduces expected error by 24.65 and 36.65 percentage points for two trained initializations. In chronological continuous-integration replay, feedback binding is positive while retention increases loss. Completed SQL studies improve substantially over an unadapted substrate but do not establish the required additional online benefit. These results characterize their declared components. The two recursive routes and their joint realization are specified here; their beneficial recursive chains and discovery efficiency remain to be evaluated.

When we speak of recursive self-improvement (RSI), are we speaking of a phenomenon, a mechanism, or a prospect? Towards autonomous and evolving intelligence, RSI is being claimed at many scales, while no single framework that formally describes these emerging instances exists. Its counterpart in the classical realm, iterative policy improvement, is characterized by generalized policy iteration (GPI), a framework of broad applicability with well-understood theoretical properties, but only where the update principle and the evaluation base lie outside the agent. In this paper, we propose Generalized Agent Iteration (GAI), a formal framework that describes iterative policy improvement and RSI as two cases of a single learning paradigm. GAI defines the agent as a configuration of modifiable components within a system and models the learning process as a cycle of agent evaluation and agent improvement. Two pivotal dials then distinguish the instances: whether the improving mechanism is part of the agent and whether the standard it is measured against is grounded outside it. The former dial delineates the boundary between GPI and RSI, and the latter determines a system's polarity as anchored, goal drift, or fully self-referential. Moreover, we use these coordinates to place existing systems on the same two axes and make the defects of recursive self-improvement statable one condition at a time. We see this paper as a first step toward exploring a formal characterization of RSI that rests on the classical account, makes existing systems comparable, and provides a principled basis for analyzing and designing new ones.

With the rapid advancement of Large Language Models (LLMs), developing effective critic modules for precise guidance has become crucial yet challenging. In this paper, we initially demonstrate that supervised fine-tuning for building critic modules (which is widely adopted in current solutions) fails to genuinely enhance models' critique abilities, producing superficial critiques with insufficient reflections and verifications. To unlock the unprecedented critique capabilities, we propose RefCritic, a long-chain-of-thought critic module based on reinforcement learning with dual rule-based rewards: (1) instance-level correctness of solution judgments and (2) refinement accuracies of the policy model based on critiques, aiming to generate high-quality evaluations with actionable feedback that effectively guides model refinement. We evaluate RefCritic on Qwen2.5-14B-Instruct and DeepSeek-R1-Distill-Qwen-14B across five benchmarks. On critique and refinement settings, RefCritic demonstrates consistent advantages across all benchmarks, e.g., 6.8\% and 7.2\% gains on AIME25 for the respective base models. Notably, under majority voting, policy models filtered by RefCritic show superior scaling with increased voting numbers. Moreover, despite training on solution-level supervision, RefCritic outperforms step-level supervised approaches on ProcessBench, a benchmark to identify erroneous steps in mathematical reasoning.

Vision-Language-Action Models (VLAs) have demonstrated remarkable generalization capabilities in real-world experiments. However, their success rates are often not on par with expert policies, and they require fine-tuning when the setup changes. In this work, we introduce Refined Policy Distillation (RPD), a novel Reinforcement Learning (RL)-based policy refinement method that bridges this performance gap through a combination of on-policy RL with behavioral cloning. The core idea of RPD is to distill and refine VLAs into compact, high-performing expert policies by guiding the student policy during RL exploration using the actions of a teacher VLA, resulting in increased sample efficiency and faster convergence. We complement our method by fine-tuned versions of Octo and OpenVLA for ManiSkill3 to evaluate RPD in simulation. While this is a key requirement for applying RL, it also yields new insights beyond existing studies on VLA performance in real-world settings. Our experimental results across various manipulation tasks show that RPD enables the RL student to learn expert policies that outperform the VLA teacher in both dense and sparse reward settings, while also achieving faster convergence than the RL baseline. Our approach is even robust to changes in camera perspective and can generalize to task variations that the underlying VLA cannot solve. Our code, dataset, VLA checkpoints, and videos are available at https://refined-policy-distillation.github.io

Large Language Models (LLMs) have shown promise in solving complex mathematical problems, yet they still fall short of producing accurate and consistent solutions. Reinforcement Learning (RL) is a framework for aligning these models with task-specific rewards, improving overall quality and reliability. Group Relative Policy Optimization (GRPO) is an efficient, value-function-free alternative to Proximal Policy Optimization (PPO) that leverages group-relative reward normalization. We introduce Iterative Group Relative Policy Optimization (iGRPO), a two-stage extension of GRPO that adds dynamic self-conditioning through model-generated drafts. In Stage 1, iGRPO samples multiple exploratory drafts and selects the highest-reward draft using the same scalar reward signal used for optimization. In Stage 2, it appends this best draft to the original prompt and applies a GRPO-style update on draft-conditioned refinements, training the policy to improve beyond its strongest prior attempt. Under matched rollout budgets, iGRPO consistently outperforms GRPO across base models (e.g., Nemotron-H-8B-Base-8K and DeepSeek-R1 Distilled), validating its effectiveness on diverse reasoning benchmarks. Moreover, applying iGRPO to OpenReasoning-Nemotron-7B trained on AceReason-Math achieves new state-of-the-art results of 85.62\% and 79.64\% on AIME24 and AIME25, respectively. Ablations further show that the refinement wrapper generalizes beyond GRPO variants, benefits from a generative judge, and alters learning dynamics by delaying entropy collapse. These results underscore the potential of iterative, self-feedback-based RL for advancing verifiable mathematical reasoning.

The OpenAI o1-series models have demonstrated that leveraging long-form Chain of Thought (CoT) can substantially enhance performance. However, the recursive thinking capabilities of Large Language Models (LLMs) remain limited, particularly in the absence of expert-curated data for distillation. In this paper, we propose AvR: Alignment via Refinement, a novel method aimed at unlocking the potential of LLMs for recursive reasoning through long-form CoT. AvR introduces a refinement process that integrates criticism and improvement actions, guided by differentiable learning techniques to optimize refinement-aware rewards. As a result, the synthesized multi-round data can be organized as a long refinement thought, further enabling test-time scaling. Experimental results show that AvR significantly outperforms conventional preference optimization methods. Notably, with only 3k synthetic samples, our method boosts the performance of the LLaMA-3-8B-Instruct model by over 20\% in win rate on AlpacaEval 2.0. Our code is available at Github (https://github.com/Banner-Z/AvR.git).

Stronger AI agents do not automatically produce better organizations: teams must also learn which work arrangements to retain and when to reconsider them. We propose a modeling specification for recursive organization improvement and evaluate it through an executable checker, a public-record mapping, and controlled simulation. The specification connects actor-visible histories, organizational memory, decision rights, and evidence-carrying change contracts. The mechanism study crosses six decision rules, three memory conditions, and three task environments under fixed resource ceilings. In a stationary environment, cumulative evidence raises balanced evaluation's normalized net value per task from 0.45224 to 0.48007. Repeated reassessment's disadvantage relative to this comparator falls from 0.01702 with reset evidence to 0.00007 with cumulative evidence. A reversal of the best workflow reveals the opposite cost: indefinite retention delays adaptation, while a finite window restores eventual performance at a transition cost. In exploratory controls, matching trial acquisition and label reuse reduces the apparent reassessment gain from 0.00607 to 0.00191. Program replacement adds no stable benefit across the tested reversal times. The study identifies evidence acquisition, reuse, and timely updating as mechanisms that must be separated from evaluator replacement when assessing organizational improvement.

Agent-compiled knowledge bases provide persistent external knowledge for large language model (LLM) agents in open-ended, knowledge-intensive downstream tasks. Yet their quality is systematically limited by incompleteness, incorrectness, and redundancy, manifested as missing evidence or cross-document links, low-confidence or imprecise claims, and ambiguous or coreference resolution issues. Such defects compound under iterative use, degrading retrieval fidelity and downstream task performance. We present DeepRefine, a general LLM-based reasoning model for agent-compiled knowledge refinement that improves the quality of any pre-constructed knowledge bases with user queries to make it more suitable for the downstream tasks. DeepRefine performs multi-turn interactions with the knowledge base and conducts abductive diagnosis over interaction history, localizes likely defects, and executes targeted refinement actions for incremental knowledge base updates. To optimize refinement policies of DeepRefine without gold references, we introduce a Gain-Beyond-Draft (GBD) reward and train the reasoning process end-to-end via reinforcement learning. Extensive experiments demonstrate consistent downstream gains over strong baselines.

Large Language Models (LLMs) have achieved remarkable success at tasks like summarization that involve a single turn of interaction. However, they can still struggle with multi-turn tasks like dialogue that require long-term planning. Previous works on multi-turn dialogue extend single-turn reinforcement learning from human feedback (RLHF) methods to the multi-turn setting by treating all prior dialogue turns as a long context. Such approaches suffer from covariate shift: the conversations in the training set have previous turns generated by some reference policy, which means that low training error may not necessarily correspond to good performance when the learner is actually in the conversation loop. In response, we introduce REgressing the RELative FUture (REFUEL), an efficient policy optimization approach designed to address multi-turn RLHF in LLMs. REFUEL employs a single model to estimate Q-values and trains on self-generated data, addressing the covariate shift issue. REFUEL frames the multi-turn RLHF problem as a sequence of regression tasks on iteratively collected datasets, enabling ease of implementation. Theoretically, we prove that REFUEL can match the performance of any policy covered by the training set. Empirically, we evaluate our algorithm by using Llama-3.1-70B-it to simulate a user in conversation with our model. REFUEL consistently outperforms state-of-the-art methods such as DPO and REBEL across various settings. Furthermore, despite having only 8 billion parameters, Llama-3-8B-it fine-tuned with REFUEL outperforms Llama-3.1-70B-it on long multi-turn dialogues. Implementation of REFUEL can be found at https://github.com/ZhaolinGao/REFUEL/, and models trained by REFUEL can be found at https://huggingface.co/Cornell-AGI.

Text-to-Image (T2I) models and Unified Multimodal Models (UMMs) have achieved remarkable progress in visual generation. However, their reliance on a single-pass generation paradigm limits their ability to handle complex prompts requiring iterative refinement. To enable multi-round Reflective Visual Generation (RVG), we formalize the Reason-Reflect-Rectify (R^3) loop as a core framework and introduce R^3-Bench, a benchmark of over 600 expert-annotated instances that quantifies iterative reasoning and rectification capabilities. Evaluation on R^3-Bench reveals a critical gap: while state-of-the-art models can identify generation errors, they fail to generate actionable rectification instructions. To bridge this gap, we propose R^3-Refiner, a dual-stage framework leveraging Group Relative Policy Optimization (GRPO) and a Hierarchical Reward Mechanism (HRM) to better align rectification with reflective reasoning. Experiments show that R^3-Refiner achieves significant improvements on R^3-Bench (+12.0% in Reflective Verdict Score, +9.0% in Rectification Score), and can be seamlessly integrated with various MLLMs to enhance the generation quality of different T2I models on GenEval++ and T2I-CompBench. Code is available at https://github.com/xiaomoguhz/R3-Bench.

Large language models (LLMs) struggle with complex, long-horizon reasoning due to instability caused by their frozen policy assumption. Current test-time scaling methods treat execution feedback merely as an external signal for filtering or rewriting trajectories, without internalizing it to improve the underlying reasoning strategy. Inspired by Popper's epistemology of "conjectures and refutations," we argue that intelligence requires real-time evolution of the model's policy through learning from failed attempts. We introduce Policy of Thoughts (PoT), a framework that recasts reasoning as a within-instance online optimization process. PoT first generates diverse candidate solutions via an efficient exploration mechanism, then uses Group Relative Policy Optimization (GRPO) to update a transient LoRA adapter based on execution feedback. This closed-loop design enables dynamic, instance-specific refinement of the model's reasoning priors. Experiments show that PoT dramatically boosts performance: a 4B model achieves 49.71% accuracy on LiveCodeBench, outperforming GPT-4o and DeepSeek-V3 despite being over 50 smaller.

State-of-the-art language models can exhibit impressive reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify when and where to refine without access to external feedback. Outcome-based Reward Models (ORMs), trained to predict correctness of the final answer indicating when to refine, offer one convenient solution for deciding when to refine. Process Based Reward Models (PRMs), trained to predict correctness of intermediate steps, can then be used to indicate where to refine. But they are expensive to train, requiring extensive human annotations. In this paper, we propose Stepwise ORMs (SORMs) which are trained, only on synthetic data, to approximate the expected future reward of the optimal policy or V^{star}. More specifically, SORMs are trained to predict the correctness of the final answer when sampling the current policy many times (rather than only once as in the case of ORMs). Our experiments show that SORMs can more accurately detect incorrect reasoning steps compared to ORMs, thus improving downstream accuracy when doing refinements. We then train global refinement models, which take only the question and a draft solution as input and predict a corrected solution, and local refinement models which also take as input a critique indicating the location of the first reasoning error. We generate training data for both models synthetically by reusing data used to train the SORM. We find combining global and local refinements, using the ORM as a reranker, significantly outperforms either one individually, as well as a best of three sample baseline. With this strategy we can improve the accuracy of a LLaMA-2 13B model (already fine-tuned with RL) on GSM8K from 53\% to 65\% when greedily sampled.

Existing reinforcement learning (RL) approaches treat large language models (LLMs) as a single unified policy, overlooking their internal mechanisms. Understanding how policy evolves across layers and modules is therefore crucial for enabling more targeted optimization and raveling out complex reasoning mechanisms. In this paper, we decompose the language model policy by leveraging the intrinsic split of the Transformer residual stream and the equivalence between the composition of hidden states with the unembedding matrix and the resulting samplable policy. This decomposition reveals Internal Layer Policies, corresponding to contributions from individual layers, and Internal Modular Policies, which align with the self-attention and feed-forward network (FFN) components within each layer. By analyzing the entropy of internal policy, we find that: (a) Early layers keep high entropy for exploration, top layers converge to near-zero entropy for refinement, with convergence patterns varying across model series. (b) LLama's prediction space rapidly converges in the final layer, whereas Qwen-series models, especially Qwen3, exhibit a more human-like, progressively structured reasoning pattern. Motivated by these findings, we propose Bottom-up Policy Optimization (BuPO), a novel RL paradigm that directly optimizes the internal layer policy during early training. By aligning training objective at lower layer, BuPO reconstructs foundational reasoning capabilities and achieves superior performance. Extensive experiments on complex reasoning benchmarks demonstrates the effectiveness of our method. Our code is available at https://github.com/Trae1ounG/BuPO.

Repository-level software engineering (SWE) comprises heterogeneous task categories, whose progress under pooled agentic reinforcement learning can be uneven: gains in some categories coincide with regressions in others, while aggregate resolution obscures these changes. Motivated by this category see-saw, we develop a category-aware expert-training and policy-integration framework. Executable task construction and SWE Labeler, an evidence-grounded multi-axis labeling system, organize the training pools. Initial category-specific RL improves average training success while leaving uneven instance-level progress, motivating explicit consolidation of successful behavior and policy-adaptive task selection. Same-origin category experts alternate long-horizon Agentic-miniRL with Refresh-Repair-Expand (RRE): the updated policy refreshes instance mastery, reuses its own verified successful trajectories for Repair SFT, and reselects tasks for further RL. Label-routed multi-teacher on-policy distillation (MOPD) consolidates the experts into one deployable student, with ReLU-gated reward extrapolation keeping only each teacher's improving direction over the reference. Expert training and policy integration require no external model to provide solution trajectories or action targets. We evaluate Pooled RL and Balanced RL, expert development, and single-model integration through aggregate and per-category resolution, the minimum category lift over each joint-RL baseline, and expert-gain recovery. The final MOPD policy achieves mean resolution of 58.04% on Pro-618 and 59.00% on SWE-bench Multilingual, improving over the base model by 5.39 and 2.78 percentage points, respectively.

Aligning large language models (LLMs) on domain-specific data remains a fundamental challenge. Supervised fine-tuning (SFT) offers a straightforward way to inject domain knowledge but often degrades the model's generality. In contrast, on-policy reinforcement learning (RL) preserves generality but fails to effectively assimilate hard samples that exceed the model's current reasoning level. Recent off-policy RL attempts improve hard sample utilization, yet they suffer from severe training instability due to the forced distribution shift toward off-policy knowledge. To reconcile effective off-policy knowledge absorption with the stability of on-policy RL, we propose Rephrasing Policy Optimization (RePO). In RePO, the policy model is prompted to first comprehend off-policy knowledge and then rephrase it into trajectories that conform to its own stylistic and parametric distribution. RePO dynamically replaces low-reward rollouts with these rephrased, high-quality trajectories. This strategy guides the model toward correct reasoning paths while strictly preserving on-policy training dynamics. Experiments on several benchmarks demonstrate that RePO improves hard-sample utilization and outperforms existing baselines, achieving state-of-the-art performance.

Performing tasks on the web presents fundamental challenges to large language models (LLMs), including combinatorially large open-world tasks and variations across web interfaces. Simply specifying a large prompt to handle all possible behaviors and states is extremely complex, and results in behavior leaks between unrelated behaviors. Decomposition to distinct policies can address this challenge, but requires carefully handing off control between policies. We propose Stacked LLM Policies for Web Actions (SteP), an approach to dynamically compose policies to solve a diverse set of web tasks. SteP defines a Markov Decision Process where the state is a stack of policies representing the control state, i.e., the chain of policy calls. Unlike traditional methods that are restricted to static hierarchies, SteP enables dynamic control that adapts to the complexity of the task. We evaluate SteP against multiple baselines and web environments including WebArena, MiniWoB++, and a CRM. On WebArena, SteP improves (14.9\% to 33.5\%) over SOTA that use GPT-4 policies, while on MiniWob++, SteP is competitive with prior works while using significantly less data. Our code and data are available at https://asappresearch.github.io/webagents-step.

In light of the burgeoning success of reinforcement learning (RL) in diverse real-world applications, considerable focus has been directed towards ensuring RL policies are robust to adversarial attacks during test time. Current approaches largely revolve around solving a minimax problem to prepare for potential worst-case scenarios. While effective against strong attacks, these methods often compromise performance in the absence of attacks or the presence of only weak attacks. To address this, we study policy robustness under the well-accepted state-adversarial attack model, extending our focus beyond only worst-case attacks. We first formalize this task at test time as a regret minimization problem and establish its intrinsic hardness in achieving sublinear regret when the baseline policy is from a general continuous policy class, Pi. This finding prompts us to refine the baseline policy class Pi prior to test time, aiming for efficient adaptation within a finite policy class Pi, which can resort to an adversarial bandit subroutine. In light of the importance of a small, finite Pi, we propose a novel training-time algorithm to iteratively discover non-dominated policies, forming a near-optimal and minimal Pi, thereby ensuring both robustness and test-time efficiency. Empirical validation on the Mujoco corroborates the superiority of our approach in terms of natural and robust performance, as well as adaptability to various attack scenarios.

Large language models (LLMs) have advanced automatic program repair (APR) to the point where agentic systems routinely resolve real-world, repository-level issues. Yet the generated patch has received little scrutiny beyond whether it passes tests. In this paper, we identify patch verbosity as a major yet overlooked concern in LLM-based APR. Characterizing 28 state-of-the-art approaches on SWE-bench Verified, we find that even successful patches are consistently larger and more complex than developer patches, with the median approach producing 121.78% more total changes, 80.91% more net changes, and 43.99% higher cyclomatic complexity. We further show that this verbosity is rooted in capability-oriented design choices such as iterative refinement and broad context, and can hardly be reduced by surface-level controls such as output format or minimality prompts. Motivated by these findings, we formulate post-generation patch refinement and propose RECAP, a lightweight, plug-and-play adapter that attaches to existing repair frameworks after generation. RECAP's refiner is trained via supervised fine-tuning and direct preference optimization with distilled reasoning traces, on a dataset of patch pairs we construct from multiple sources. Across four host systems, prompting, commit-untangling, and minimality-aware baselines reduce patch size only by sacrificing 49 to 217 resolved instances. In contrast, RECAP achieves a substantially better size-correctness tradeoff, cutting average total changes from +242.14% to +4.24% and net changes from +348.24% to -39.75% relative to developer patches while preserving or improving resolution by up to 42 instances. Our results indicate that minimality cannot be simply reduced to syntactic compression, and that decoupling minimization from generation offers a practical path to more reviewable repairs.

Recursive self-improvement (RSI) aims to transform interaction experience into persistent improvements, yet external feedback is costly and world-model predictions may become unreliable as policies evolve. We introduce RSI-Anything, a domain-general framework built on JEPA-Anything that uses predictive world models to guide action and learning-data selection. Observed feedback drives policy or workflow improvement and conditional world-model adaptation, while component and compatibility checks govern the retention of updated policy-model pairs. Across diverse computational and scientific domains, RSI-Anything demonstrates substantial gains. In code repair, with the coder fixed, success increases from 26.3% with a static verifier to 29.2% through predictive selection and 31.2% after world-model adaptation, at comparable test usage. Graphical user interface (GUI) evaluations showed higher task completion, while average actions decrease by 39.4%. Across five successive policy versions, laboratory-planning scores more than double from 21.80% to 46.01%. In reaction optimization, RSI-Anything achieves 96.15% mean best observed yield versus 82.16% for Bayesian optimization under the same 40-experiment budget. An end-to-end immune-science application further connects workflow evolution and predictive modeling with therapeutic hypothesis generation. These results demonstrate how predictive world models and retained system updates enable recursive improvement across diverse environments.

In long-horizon LLM agent reinforcement learning, weak policies often repeat similar failures, producing uninformative rollout trajectories and limiting effective policy optimization. Existing skill-centric methods improve exploration by optimizing, filtering, or internalizing reusable skills. However, they remain centered on the skills themselves rather than being designed as adaptive training-time support for the evolving policy. To address this, we propose a policy-centric training paradigm that reframes skills as a dynamic training scaffold. Our framework, Pats, converts rollout groups from the latest policy into evidence cards and uses task-specific evaluation to adjust the context used in subsequent rollouts. Concrete guidance helps weak policies to complete challenging tasks. As policy improves, redundant context is revised or removed to reduce reliance on explicit guidance while preserving useful rollout variation. The policy is optimized with environmental rewards using standard RLVR, and the training scaffold is discarded at deployment. On ALFWorld and WebShop, Pats improves over strong baselines by up to 18.6%. Across seven search-augmented QA benchmarks, it remains competitive while using 32.1% fewer prompt tokens than the baseline.

Reinforcement Learning with Verifiable Rewards (RLVR) is increasingly viewed as a tree pruning mechanism. However, we identify a systemic pathology termed Recursive Space Contraction (RSC), an irreversible collapse driven by the combined dynamics of positive sharpening and negative squeezing, where the sampling probability of valid alternatives vanishes. While Kullback-Leibler (KL) regularization aims to mitigate this, it imposes a rigid Shape Matching constraint that forces the policy to mimic the reference model's full density, creating a gradient conflict with the sharpening required for correctness. We propose Anchored Policy Optimization (APO), shifting the paradigm from global Shape Matching to Support Coverage. By defining a Safe Manifold based on the reference model's high-confidence support, APO permits aggressive sharpening for efficiency while selectively invoking a restorative force during error correction to prevent collapse. We theoretically derive that APO serves as a gradient-aligned mechanism to maximize support coverage, enabling an Elastic Recovery that re-inflates valid branches. Empirical evaluations on mathematical benchmarks demonstrate that APO breaks the accuracy-diversity trade-off, significantly improving Pass@1 while restoring the Pass@K diversity typically lost by standard policy gradient methods.

Recursive self-improvement (RSI) lets a system improve the model-building machinery from its own failures, so every later model inherits the gain. Yet RSI has been validated almost exclusively on coding and formal benchmarks such as science QA and mathematics. This format bound limits RSI to improvement within a machine-checkable slice, not general capability where questions are open and correctness is settled by argument, replication, or measurement. We argue RSI must next operate across real, diverse scientific, engineering, and meta-scientific domains, not where formal evaluation is merely tractable. To that end we present MetaRSI-v1, where improvement is the scheduled composition of three typed operators over one unified paradigm. Data-RSI amplifies existing competence and marks its boundary; Harness-RSI edits a five-slot scaffold without touching weights; Model-RSI internalizes capability into parameters through bounded training. Sharing one loop kernel and artifact vocabulary, they make data, scaffold, and model changes composable rather than exclusive. A two-axis optimizer jointly decides operator order and each operator's proposal policy, while a meta-level policy revises the schedule across terms. We validate MetaRSI-v1 under the field's standard evaluations, on code and closed-form science, with no external teacher: the target model plays every role in its own loop. MetaRSI-v1 reframes self-improvement from a single-surface edit to a composition across the full model-production pipeline, opening two paths: a model route internalizing capability through training, and a harness route leaving weights untouched and thus extending self-improvement to any model reachable through an interface, with Data-RSI redefined as the shared substrate feeding both. The framework further yields refutable laws on where loops exist, how operators compose, and what supervision buys.

RLVR has substantially improved the reasoning capabilities of LLMs. However, existing methods typically parameterize temporal progression in the Markov Decision Process by token-by-token generation, despite the highly non-uniform information flow along autoregressive trajectories. In this paper, we propose InfoPPO, which reparameterizes temporal progression using information density rather than raw token count. This reparameterization induces a common state-dependent structure for both temporal credit propagation and policy updates. InfoPPO restores the effectiveness of non-trivial discounting in long-horizon reasoning, retaining effective-horizon contraction while avoiding excessive attenuation of terminal supervision over long token sequences. Moreover, the information-time policy-improvement analysis naturally leads to a state-dependent update constraint, which we implement through adaptive clipping. By adapting the clipping threshold at each token position to the information density of its corresponding state, this mechanism enables more targeted policy updates while preserving proximal control. Theoretically, we extend performance-difference and policy-improvement analyses to the information-time MDP, deriving a policy-improvement lower bound when policy changes are regulated by information density. We further connect the general information-time analysis to practical LLM policy optimization by relating state-wise information density to local policy movement, while also providing theoretical grounding for the adaptive update mechanism. Experiments on Qwen3 models demonstrate consistent gains over competitive baselines across five challenging competition-style mathematical reasoning benchmarks. InfoPPO also maintains stable accuracy and response length across non-trivial discount settings under which token-time PPO deteriorates.

We introduce Recursive Agent Optimization (RAO), a reinforcement learning approach for training recursive agents: agents that can spawn and delegate sub-tasks to new instantiations of themselves recursively. Recursive agents implement an inference-time scaling algorithm that naturally allows agents to scale to longer contexts and generalize to more difficult problems via divide-and-conquer. RAO provides a method to train models to best take advantage of such recursive inference, teaching agents when and how to delegate and communicate. We find that recursive agents trained in this way enjoy better training efficiency, can scale to tasks that go beyond the model's context window, generalize to tasks much harder than the ones the agent was trained on, and can enjoy reduced wall-clock time compared to single-agent systems.

Large Language Models' (LLM) reasoning can be improved using test-time aggregation strategies, i.e., generating multiple samples and voting among generated samples. While these improve performance, they often reach a saturation point. Refinement offers an alternative by using LLM-generated feedback to improve solution quality. However, refinement introduces 3 key challenges: (1) Excessive refinement: Uniformly refining all instances can over-correct and reduce the overall performance. (2) Inability to localize and address errors: LLMs have a limited ability to self-correct and struggle to identify and correct their own mistakes. (3) Insufficient refinement: Deciding how many iterations of refinement are needed is non-trivial, and stopping too soon could leave errors unaddressed. To tackle these issues, we propose MAgICoRe, which avoids excessive refinement by categorizing problem difficulty as easy or hard, solving easy problems with coarse-grained aggregation and hard ones with fine-grained and iterative multi-agent refinement. To improve error localization, we incorporate external step-wise reward model (RM) scores. Moreover, to ensure effective refinement, we employ a multi-agent loop with three agents: Solver, Reviewer (which generates targeted feedback based on step-wise RM scores), and the Refiner (which incorporates feedback). To ensure sufficient refinement, we re-evaluate updated solutions, iteratively initiating further rounds of refinement. We evaluate MAgICoRe on Llama-3-8B and GPT-3.5 and show its effectiveness across 5 math datasets. Even one iteration of MAgICoRe beats Self-Consistency by 3.4%, Best-of-k by 3.2%, and Self-Refine by 4.0% while using less than half the samples. Unlike iterative refinement with baselines, MAgICoRe continues to improve with more iterations. Finally, our ablations highlight the importance of MAgICoRe's RMs and multi-agent communication.

Many reinforcement learning systems, from fleet management to traffic signal control, must serve an objective that changes dynamically after deployment, and retraining a policy for each new objective is prohibitively expensive. For a single agent, this problem is well understood: successor features with generalized policy improvement, together with their universal extension, recombine a library of learned policies into a policy for any new objective, with a guarantee that the result is never worse than any policy in the library. However, multi-agent transfer has received far less attention, and the common practice of letting each agent recombine its own library independently inherits the recipe but not the guarantee. We prove that this independent composition can produce joint behavior strictly worse than every policy in the library, because recombining teammates changes the environment each agent faces and invalidates the values it relies on, a failure with no single-agent counterpart. We further show that the only unconditionally safe fixed rule is synchronized composition, which moves the whole team to one jointly trained policy but cannot serve objectives that assign different goals to different agents. To attain safety and flexibility at once, we propose MA-USFA, a hierarchical method with two layers: a lower layer of universal successor feature approximators that predicts each agent's successor features while conditioned on its teammates' objectives, and an upper composer that selects, across agents, which library entry each agent should follow and supplies the cross-agent correction a per-agent value cannot represent. Trained once over the distribution of objectives, it is applied at deployment with no per-task adaptation.

Recent advances in reinforcement learning (RL) have significantly enhanced the agentic capabilities of large language models (LLMs). In long-term and multi-turn agent tasks, existing approaches driven solely by outcome rewards often suffer from the problem of sparse supervision. To address the challenge, we propose Tree-based Group Relative Policy Optimization (Tree-GRPO), a grouped agent RL method based on tree search, where each tree node represents the complete agent interaction step. By sharing common prefixes, the tree search sampling increases the number of rollouts achievable within a fixed budget of tokens or tool calls. Moreover, we find that the tree-structured trajectory naturally allows the construction of step-wise process supervised signals even using only the outcome reward. Based on this, Tree-GRPO estimates the grouped relative advantages both on intra-tree and inter-tree levels. Through theoretical analysis, we demonstrate that the objective of intra-tree level group relative policy optimization is equivalent to that of step-level direct preference learning. Experiments across 11 datasets and 3 types of QA tasks demonstrate the superiority of the proposed tree-based RL over the chain-based RL method.

Large language models show strong reasoning ability, but their internal reasoning process can remain unstable in complex multi-step settings, where early hidden-state errors may propagate to incorrect predictions. We propose ReLAR, a reinforcement-guided latent refinement framework that iteratively updates hidden representations before decoding. ReLAR maintains a compact latent reasoning state and uses learned depth and action controllers to adaptively determine both the number and direction of refinement steps. The controllers are trained with a policy gradient objective based on step-wise likelihood improvement, enabling efficient input-dependent reasoning without explicit chain-of-thought generation. Experiments on medical, mathematical, multi-hop reasoning, and open-ended generation benchmarks show that ReLAR improves accuracy, generation quality, and reasoning stability with substantially lower inference overhead than explicit reasoning baselines.

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-based policies for continuous control robotic navigation tasks often fail to adapt to changes in the environment during real-time deployment, which may result in catastrophic failures. To address this limitation, we propose a novel approach called RE-MOVE (REquest help and MOVE on), which uses language-based feedback to adjust trained policies to real-time changes in the environment. In this work, we enable the trained policy to decide when to ask for feedback and how to incorporate feedback into trained policies. RE-MOVE incorporates epistemic uncertainty to determine the optimal time to request feedback from humans and uses language-based feedback for real-time adaptation. We perform extensive synthetic and real-world evaluations to demonstrate the benefits of our proposed approach in several test-time dynamic navigation scenarios. Our approach enable robots to learn from human feedback and adapt to previously unseen adversarial situations.

Training deep research agents, namely systems that plan, search, evaluate evidence, and synthesize long-form reports, pushes reinforcement learning beyond the regime of verifiable rewards. Their outputs lack ground-truth answers, their trajectories span many tool-augmented decisions, and standard post-training offers little mechanism for turning past attempts into reusable experience. In this work, we argue that rubrics should serve not merely as final-answer evaluators, but as the shared interface that structures policy execution, judge feedback, and agent memory. Based on this view, we introduce RubricEM, a rubric-guided reinforcement learning framework that combines stagewise policy decomposition with reflection-based meta-policy evolution. RubricEM first makes research trajectories stage-aware by conditioning planning, evidence gathering, review, and synthesis on self-generated rubrics. It then assigns credit with Stage-Structured GRPO, which uses stagewise rubric judgments to provide denser semantic feedback for long-horizon optimization. In parallel, RubricEM trains a shared-backbone reflection meta-policy that distills judged trajectories into reusable rubric-grounded guidance for future attempts. The resulting RubricEM-8B achieves strong performance across four long-form research benchmarks, outperforming comparable open models and approaching proprietary deep-research systems. Beyond final performance, we perform thorough analyses to understand the key ingredients of RubricEM.

Aiming to produce reinforcement learning (RL) policies that are human-interpretable and can generalize better to novel scenarios, Trivedi et al. (2021) present a method (LEAPS) that first learns a program embedding space to continuously parameterize diverse programs from a pre-generated program dataset, and then searches for a task-solving program in the learned program embedding space when given a task. Despite the encouraging results, the program policies that LEAPS can produce are limited by the distribution of the program dataset. Furthermore, during searching, LEAPS evaluates each candidate program solely based on its return, failing to precisely reward correct parts of programs and penalize incorrect parts. To address these issues, we propose to learn a meta-policy that composes a series of programs sampled from the learned program embedding space. By learning to compose programs, our proposed hierarchical programmatic reinforcement learning (HPRL) framework can produce program policies that describe out-of-distributionally complex behaviors and directly assign credits to programs that induce desired behaviors. The experimental results in the Karel domain show that our proposed framework outperforms baselines. The ablation studies confirm the limitations of LEAPS and justify our design choices.

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.

Training multi-turn agentic workflows with reinforcement learning (RL) enables large language models to perform complex reasoning, use external tools, and conduct iterative search beyond single-turn settings. Yet multi-turn RL training remains highly unstable, often causing severe performance degradation as the number of turns increases. Through theoretical analysis, we identify three tightly coupled sources of instability: rollout-training context mismatch, weak turn-level credit assignment under sparse terminal rewards, and asynchronous policy drift when short and long trajectories are optimized under different policy versions. We show that these issues share a common structural origin in flattened trajectory optimization and address them through a unified reverse-turn formulation. We propose Reverse-Turn Policy Optimization (RTPO), which organizes multi-turn rollouts as sparse reverse trees and performs turn-level policy updates in temporal reverse order, aligning each decision with its downstream continuation. RTPO enables causally consistent turn-level credit assignment and on-policy continuation to control asynchronous drift. We provide theoretical guarantees showing that RTPO eliminates context mismatch and asynchronous drift under the proposed turn-level formulation, reduces credit bias, and converges to recursive optimality. Experiments on multi-turn agentic RL benchmarks show that RTPO improves upon trajectory- and turn-level baselines by 21.50% and 10.76%, respectively, highlighting its potential to support more stable training for tool-using agents.

We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4times faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.

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.

Reinforcement learning is a framework for learning to act sequentially in an unknown environment. We propose a natural approach for modeling policy structure in policy gradients. The key idea is to optimize for a subset of future rewards: smaller subsets represent simpler policies, which can be learned more reliably because their empirical gradient estimates are more accurate. Our approach allows for modeling and comparison of different policy classes, including full planning, greedy, K-step lookahead, and segment policies. We evaluate the policies empirically on multiple persona-alignment conversational problems. Different policies excel in different problems, reflecting their different characteristics and highlighting the importance of our studied policy class.

Multimodal deep search requires an agent to solve open-world problems by chaining search, tool use, and visual reasoning over evolving textual and visual context. Two bottlenecks limit current systems. First, existing tool-use harnesses treat images returned by search, browsing, or transformation as transient outputs, so intermediate visual evidence cannot be re-consumed by later tools. Second, training data is usually built by fixed curation recipes that cannot track the target agent's evolving capability. To address these challenges, we first introduce a visual-native agent harness centered on an image bank reference protocol, which registers every tool-returned image as an addressable reference and makes intermediate visual evidence reusable by later tools. On top of this harness, On-policy Data Evolution (ODE) runs a closed-loop data generator that refines itself across rounds from rollouts of the policy being trained. This per-round refinement makes each round's data target what the current policy still needs to learn. The same framework supports both diverse supervised fine-tuning data and policy-aware reinforcement learning data curation, covering the full training lifecycle of the target agent. Across 8 multimodal deep search benchmarks, ODE improves the Qwen3-VL-8B agent from 24.9% to 39.0% on average, surpassing Gemini-2.5 Pro in standard agent-workflow setting (37.9%). At 30B, ODE raises the average score from 30.6% to 41.5%. Further analyses validate the effectiveness of image-bank reuse, especially on complex tasks requiring iterative visual refinement, while rollout-feedback evolution yields more grounded SFT traces and better policy-matched RL tasks than static synthesis.

Generalist manipulation policies increasingly take the form of action-chunking flow policies built on large pretrained backbones. Such chunks run open-loop, so the policy cannot react to sensory input arriving mid-execution, sacrificing reactivity. Replanning more often would restore it, but the perception-to-action pipeline (a large backbone plus multiple denoising steps) is too slow: this latency forbids frequent replanning and leaves committed actions stale, making such policies ill-suited for dynamic, closed-loop control. We present πR^2, which makes these policies reactive and real-time while retaining large backbones, expressive multi-modal policies, and multi-action prediction. Built on the per-position noise schedule of diffusion forcing, πR^2 contributes two ideas. First, it splits conditioning into a fast channel (proprioception, fresh every tick) and an asynchronously updated slow channel (vision-language features), so the policy reacts to proprioception within a chunk while tolerating stale vision. Second, a latency-adaptive flow schedule treats in-flight actions as inpainting conditioning and emits actions in one denoising step per call, letting one trained model adapt to varying hardware latency. Requiring minimal modification to existing architectures, πR^2 can be finetuned from a pretrained policy: applied to GR00T-N1.7 on a real xArm6+XHand platform, it replans closed-loop roughly 4times faster than the base policy (~25Hz on an A5000 GPU), acting on a fresh observation every 40ms. Across simulation and real-world manipulation tasks, πR^2 improves the success rate by up to 23% in simulation and 30% in the real world over the strongest baseline. Project page: https://pi-r2-flow.github.io/

Generating natural language explanations for recommendations has become increasingly important in recommender systems. Traditional approaches typically treat user reviews as ground truth for explanations and focus on improving review prediction accuracy by designing various model architectures. However, due to limitations in data scale and model capability, these explanations often fail to meet key user-centric aspects such as factuality, personalization, and sentiment coherence, significantly reducing their overall helpfulness to users. In this paper, we propose a novel paradigm that refines initial explanations generated by existing explainable recommender models during the inference stage to enhance their quality in multiple aspects. Specifically, we introduce a multi-agent collaborative refinement framework based on large language models. To ensure alignment between the refinement process and user demands, we employ a plan-then-refine pattern to perform targeted modifications. To enable continuous improvements, we design a hierarchical reflection mechanism that provides feedback on the refinement process from both strategic and content perspectives. Extensive experiments on three datasets demonstrate the effectiveness of our framework.

Current Large Language Model (LLM) agents show strong performance in tool use, but lack the crucial capability to systematically learn from their own experiences. While existing frameworks mainly focus on mitigating external knowledge gaps, they fail to address a more fundamental limitation: the inability to iteratively refine problem-solving strategies. In this work, we introduce EvolveR, a framework designed to enable agent to self-improve through a complete, closed-loop experience lifecycle. This lifecycle comprises two key stages: (1) Offline Self-Distillation, where the agent's interaction trajectories are synthesized into a structured repository of abstract, reusable strategic principles; (2) Online Interaction, where the agent interacts with tasks and actively retrieves distilled principles to guide its decision-making, accumulating a diverse set of behavioral trajectories. This loop employs a policy reinforcement mechanism to iteratively update the agent based on its performance. We demonstrate the effectiveness of EvolveR on complex multi-hop question-answering benchmarks, where it achieves superior performance over strong agentic baselines. Our work presents a comprehensive blueprint for agents that learn not only from external data but also from the consequences of their own actions, paving the way for more autonomous and continuously improving systems. Code is available at https://github.com/Edaizi/EvolveR.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the complex reasoning capabilities of Large Reasoning Models. However, standard outcome-based supervision suffers from a critical limitation that penalizes trajectories that are largely correct but fail due to several missteps as heavily as completely erroneous ones. This coarse feedback signal causes the model to discard valuable largely correct rollouts, leading to a degradation in rollout diversity that prematurely narrows the exploration space. Process Reward Models have demonstrated efficacy in providing reliable step-wise verification for test-time scaling, naively integrating these signals into RLVR as dense rewards proves ineffective.Prior methods attempt to introduce off-policy guided whole-trajectory replacement that often outside the policy model's distribution, but still fail to utilize the largely correct rollouts generated by the model itself and thus do not effectively mitigate the narrowing of the exploration space. To address these issues, we propose SCOPE (Step-wise Correction for On-Policy Exploration), a novel framework that utilizes Process Reward Models to pinpoint the first erroneous step in suboptimal rollouts and applies fine-grained, step-wise off-policy rectification. By applying precise refinement on partially correct rollout, our method effectively salvages partially correct trajectories and increases diversity score by 13.5%, thereby sustaining a broad exploration space. Extensive experiments demonstrate that our approach establishes new state-of-the-art results, achieving an average accuracy of 46.6% on math reasoning and exhibiting robust generalization with 53.4% accuracy on out-of-distribution reasoning tasks.

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.

Large language models have demonstrated impressive reasoning capabilities but are inherently limited by their knowledge reservoir. Retrieval-augmented reasoning mitigates this limitation by allowing LLMs to query external resources, but existing methods often retrieve irrelevant or noisy information, hindering accurate reasoning. In this paper, we propose AutoRefine, a reinforcement learning post-training framework that adopts a new ``search-and-refine-during-think'' paradigm. AutoRefine introduces explicit knowledge refinement steps between successive search calls, enabling the model to iteratively filter, distill, and organize evidence before generating an answer. Furthermore, we incorporate tailored retrieval-specific rewards alongside answer correctness rewards using group relative policy optimization. Experiments on single-hop and multi-hop QA benchmarks demonstrate that AutoRefine significantly outperforms existing approaches, particularly in complex, multi-hop reasoning scenarios. Detailed analysis shows that AutoRefine issues frequent, higher-quality searches and synthesizes evidence effectively.

Off-policy reinforcement learning (RL) has proven to be a powerful framework for guiding agents' actions in environments with stochastic rewards and unknown or noisy state dynamics. In many real-world settings, these agents must operate in multiple environments, each with slightly different dynamics. For example, we may be interested in developing policies to guide medical treatment for patients with and without a given disease, or policies to navigate curriculum design for students with and without a learning disability. Here, we introduce nested policy fitted Q-iteration (NFQI), an RL framework that finds optimal policies in environments that exhibit such a structure. Our approach develops a nested Q-value function that takes advantage of the shared structure between two groups of observations from two separate environments while allowing their policies to be distinct from one another. We find that NFQI yields policies that rely on relevant features and perform at least as well as a policy that does not consider group structure. We demonstrate NFQI's performance using an OpenAI Gym environment and a clinical decision making RL task. Our results suggest that NFQI can develop policies that are better suited to many real-world clinical environments.

Test-time training (TTT) adapts model parameters on unlabeled test instances during inference time, which continuously extends capabilities beyond the reach of offline training. Despite initial gains, existing TTT methods for LRMs plateau quickly and do not benefit from additional test-time compute. Without external calibration, the self-generated reward signal increasingly drifts as the policy model evolves, leading to both performance plateaus and diversity collapse. We propose TEMPO, a TTT framework that interleaves policy refinement on unlabeled questions with periodic critic recalibration on a labeled dataset. By formalizing this alternating procedure through the Expectation-Maximization (EM) algorithm, we reveal that prior methods can be interpreted as incomplete variants that omit the crucial recalibration step. Reintroducing this step tightens the evidence lower bound (ELBO) and enables sustained improvement. Across diverse model families (Qwen3 and OLMO3) and reasoning tasks, TEMPO improves OLMO3-7B on AIME 2024 from 33.0% to 51.1% and Qwen3-14B from 42.3% to 65.8%, while maintaining high diversity.

LLM agents' capabilities depend not only on their underlying models but also on their execution harnesses. Recursive self-improvement (RSI) offers a promising approach to automatically evolve these harnesses. However, deploying RSI in open-world settings still faces two critical challenges. First, open-world tasks are typically unseen during the harness design phase and novel at test time, leaving no ground-truth verifiers to reliably guide online harness edits. Second, the RSI process remains highly task-specific and fails to generalize to novel scenarios. We introduce Harness^2, a plug-and-play, recursive agent harnessing framework that addresses these challenges through two connected levels of recursion. Task-level recursion refines the current task's harness using a contrastive Propose-Probe-Compose step that reliably guides edits without ground-truth verifiers, and can be scaled further via parallel or sequential recursion. Harnessing-level recursion then extracts experience from these edits to update a continual improvement harness, enabling the agent to better adapt to future tasks. Across three professional benchmarks and four model-harness configurations, a single step consistently improves GLM-5 and Gemini 3.5 Flash over their base harnesses, yielding gains of up to 11.5 points on WorkBuddy-Bench, 4.5 points on JobBench, and 11.8 percentage points on LAB, with further gains as the task-level recursion budget increases.

Contemporary progress in large language models (LLMs) has revealed notable inferential capacities via reinforcement learning (RL) employing verifiable reward, facilitating the development of O1 and R1-like reasoning models. Directly training from base models with RL is called zero-RL. However, previous works rely upon activating LLMs' inherent capacities through fixed prompt templates. This strategy introduces substantial sampling inefficiencies for weak LLMs, as the majority of problems generate invalid outputs during accuracy-driven filtration in reasoning tasks, which causes a waste of samples. To solve this issue, we propose Cog-Rethinker, a novel hierarchical metacognitive RL framework for LLM reasoning. Our Cog-Rethinker mainly focuses on the rollout procedure in RL training. After the direct rollout, our Cog-Rethinker improves sample utilization in a hierarchical metacognitive two-stage framework. By leveraging human cognition during solving problems, firstly, it prompts policy to decompose zero-accuracy problems into subproblems to produce final reasoning results. Secondly, with zero-accuracy problems in previous rollout stage, it further prompts policy to refine these answers by referencing previous wrong solutions. Moreover, to enable cold-start of the two new reasoning patterns and maintain train-test consistency across prompt templates, our Cog-Rethinker applies supervised fine-tuning on the policy using correct samples of the two stages with direct rollout template. Experimental results demonstrate Cog-Rethinker's superior performance on various mathematical reasoning benchmarks, we also analyzed its improved sample efficiency that accelerates convergence compared to baseline methods.

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

We study environment scaling as a way to increase agent-benchmark difficulty while holding core task objectives fixed. Our framework, Recursive Environment Scaling (RES), transforms existing benchmark environments while preserving their objectives and completion requirements. A proposer changes information access, resource relations, and execution dependencies; execution-grounded checks validate the resulting candidate, and accepted changes are inherited across rounds. This produces related environments for paired evaluation and training-trajectory collection. Experiments on 294 initial tasks from three benchmarks show lower task success for all six evaluation models, with decreases of 57.14--77.14 percentage points on Claw-Eval-Live. With equal trajectory counts and identical optimization settings, fine-tuning on RES trajectories outperforms original-trajectory SFT in all nine model--benchmark comparisons by 7.00--14.61 percentage points. Ablations identify recursive inheritance and dependency composition as important contributors to increased difficulty. Together, these results support environment scaling for both agent evaluation and training.

Recursive self-improvement, the participation of AI systems in improving their own capabilities, is beginning to move from theoretical prospect to practice, posing both challenges and opportunities for safety alignment. Models evolve through frequent updates, and their safety alignment requires continual adaptation to each new checkpoint. Meanwhile, with evolving red-teaming methods exposing new vulnerabilities, safety improvement for each checkpoint needs to mitigate exposed vulnerabilities and generalize to risks not yet revealed. Following R^2AI, we term these goals resistance to known threats and resilience to unforeseen risks. Recursive self-improvement, in turn, inspires an approach to both goals: safety alignment could likewise advance through successive rounds of evaluation and update. We therefore introduce ReSI, a recursive safety improvement framework that implements this approach through automated research. In each round, ReSI applies diverse red-teaming methods to identify vulnerabilities in the current target model, develops training recipes, and promotes the update with the largest safety gain among those passing a Pareto gate on capability retention as the next target model. Across four dense and mixture-of-experts models, ReSI matches or exceeds evaluated frontier models on in-distribution and out-of-distribution safety benchmarks, and outperforms alignment baselines on nearly all safety evaluations while largely preserving general capabilities. In particular, ReSI reduces the mean X-Teaming attack success rate across the four models from 86.01% to 31.45%, well below GPT-5.6-Luna's leading frontier result of 56.69%, indicating stronger resilience to attacks unseen during training. These findings support recursive safety improvement as a practical path toward resistant and resilient AI.

Large Multimodal Models (LMMs) have achieved remarkable success in vision-language tasks, yet their vast parameter counts are often underutilized during both training and inference. In this work, we embrace the idea of looping back to move forward: reusing model parameters through recursive refinement to extract stronger multimodal representations without increasing model size. We propose RecursiveVLM, a recursive Transformer architecture tailored for LMMs. Two key innovations enable effective looping: (i) a Recursive Connector that aligns features across recursion steps by fusing intermediate-layer hidden states and applying modality-specific projections, respecting the distinct statistical structures of vision and language tokens; (ii) a Monotonic Recursion Loss that supervises every step and guarantees performance improves monotonically with recursion depth. This design transforms recursion into an on-demand refinement mechanism: delivering strong results with few loops on resource-constrained devices and progressively improving outputs when more computation resources are available. Experiments show consistent gains of +3% over standard Transformers and +7% over vanilla recursive baselines, demonstrating that strategic looping is a powerful path toward efficient, deployment-adaptive LMMs.

Real-world tasks require decisions at varying granularities, and humans excel at this by leveraging a unified cognitive representation where planning is fundamentally understood as a high-level form of action. However, current Large Language Model (LLM)-based agents lack this crucial capability to operate fluidly across decision granularities. This limitation stems from existing paradigms that enforce a rigid separation between high-level planning and low-level action, which impairs dynamic adaptability and limits generalization. We propose ReCode (Recursive Code Generation), a novel paradigm that addresses this limitation by unifying planning and action within a single code representation. In this representation, ReCode treats high-level plans as abstract placeholder functions, which the agent then recursively decomposes into finer-grained sub-functions until reaching primitive actions. This recursive approach dissolves the rigid boundary between plan and action, enabling the agent to dynamically control its decision granularity. Furthermore, the recursive structure inherently generates rich, multi-granularity training data, enabling models to learn hierarchical decision-making processes. Extensive experiments show ReCode significantly surpasses advanced baselines in inference performance and demonstrates exceptional data efficiency in training, validating our core insight that unifying planning and action through recursive code generation is a powerful and effective approach to achieving universal granularity control. The code is available at https://github.com/FoundationAgents/ReCode.

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

Autonomous agents are increasingly expected to improve executable policies through feedback, yet existing evaluations often collapse this process into a final score or confound it with open-ended software-engineering progress. We introduce Autonomous Policy Evolution, a controlled evaluation setting in which a harness-model agent repeatedly edits an executable policy system under a fixed interaction budget. We instantiate this setting in EvoPolicyGym, a benchmark built from compact interactive RL environments that evaluates how agents iteratively improve explored policies. On the EvoPolicyGym suite, GPT-5.5 achieves the strongest aggregate rank score and top-two performance on all 16 environments. Beyond leaderboard results, EvoPolicyGym also provides trajectory-level diagnostics that distinguish how agents allocate budget, convert feedback into parametric tuning. These analyses show that strong autonomous policy evolution depends not only on isolated task wins, but on discovering task-appropriate mechanisms and refining policies under bounded feedback.

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Explanations of these algorithms often assume prior knowledge, lack critical details, and/or are overly generalized and complex. Here, each method is discussed and developed step by step using simplified and explicit notation focused on LLMs, aiming to eliminate ambiguity and provide a clear and intuitive understanding of the concepts. By minimizing detours into the broader RL literature and connecting concepts to LLMs, we eliminate superfluous abstractions and reduce cognitive overhead. Following this exposition, we provide a literature review of new techniques and approaches beyond those detailed. Finally, new ideas for research and exploration in the form of GRAPE (Generalized Relative Advantage Policy Evolution) are presented.

Unified multimodal large language models (MLLMs) and multi-agent systems have advanced visual generation. However, three limitations remain. (1) Existing methods often distill task-specific experience with limited generalizability. (2) Reflection is often deferred until task completion. (3) Knowledge is often acquired only in response to downstream task demands. To address these limitations, we introduce OmniHarness, a framework for generalizable visual generation via symbolic policy learning. OmniHarness abstracts verified executions into symbolic policies for visual generation task families, capturing shared procedures and applicability conditions while removing instance-specific inputs. The harness instantiates, adapts, and composes these policies for new tasks. Intermediate verification guides refinement and failure recovery during execution. Through self-directed inquiry, OmniHarness autonomously generates and executes practice tasks near its capability limits before downstream objectives are specified. Execution feedback continually refines the policies while model parameters remain fixed. Experiments across six benchmarks, three MLLM backbones, and three visual agent frameworks demonstrate strong performance and continual capability expansion. On ComfyBench's Creative tasks, OmniHarness achieves a 95.0% resolve rate, exceeding the strongest baseline by 27.5 percentage points. Frozen policy snapshots improve existing visual agent systems through plug-and-play reuse.

Policy gradient methods rely on a baseline to measure the relative advantage of an action, ensuring the model reinforces behaviors that outperform its current average capability. In the training of Large Language Models (LLMs) using Actor-Critic methods (e.g., PPO), this baseline is typically estimated by a Value Model (Critic) often as large as the policy model itself. However, as the policy continuously evolves, the value model requires expensive, synchronous incremental training to accurately track the shifting capabilities of the policy. To avoid this overhead, Group Relative Policy Optimization (GRPO) eliminates the coupled value model by using the average reward of a group of rollouts as the baseline; yet, this approach necessitates extensive sampling to maintain estimation stability. In this paper, we propose V_0, a Generalist Value Model capable of estimating the expected performance of any model on unseen prompts without requiring parameter updates. We reframe value estimation by treating the policy's dynamic capability as an explicit context input; specifically, we leverage a history of instruction-performance pairs to dynamically profile the model, departing from the traditional paradigm that relies on parameter fitting to perceive capability shifts. Focusing on value estimation at State Zero (i.e., the initial prompt, hence V_0), our model serves as a critical resource scheduler. During GRPO training, V_0 predicts success rates prior to rollout, allowing for efficient sampling budget allocation; during deployment, it functions as a router, dispatching instructions to the most cost-effective and suitable model. Empirical results demonstrate that V_0 significantly outperforms heuristic budget allocation and achieves a Pareto-optimal trade-off between performance and cost in LLM routing tasks.

Reinforcement learning fine-tuning (RLFT) is a dominant paradigm for improving pretrained policies for downstream tasks. These pretrained policies, trained on large datasets, produce generations with a broad range of promising but unrefined behaviors. Often, a critical failure mode of RLFT arises when policies lose this diversity and collapse into a handful of easily exploitable outputs. This convergence hinders exploration, which is essential for expanding the capabilities of the pretrained policy and for amplifying the benefits of test-time compute scaling. To address this, we introduce an objective for policy gradient methods that explicitly enforces the exploration and refinement of diverse generations, which we call a polychromic objective. We then show how proximal policy optimization (PPO) can be adapted to optimize this objective. Our method (1) employs vine sampling to collect on-policy rollouts and (2) modifies the advantage function to reflect the advantage under our new objective. Experiments on BabyAI, Minigrid, and Algorithmic Creativity show that our method improves success rates by reliably solving a larger set of environment configurations and generalizes better under large perturbations. Moreover, when given multiple attempts in pass@k experiments, the policy achieves substantially higher coverage, demonstrating its ability to maintain and exploit a diverse repertoire of strategies.

Recent advances in flow-based offline reinforcement learning (RL) have achieved strong performance by parameterizing policies via flow matching. However, they still face critical trade-offs among expressiveness, optimality, and efficiency. In particular, existing flow policies interpret the L_2 regularization as an upper bound of the 2-Wasserstein distance (W_2), which can be problematic in offline settings. This issue stems from a fundamental geometric mismatch: the behavioral policy manifold is inherently anisotropic, whereas the L_2 (or upper bound of W_2) regularization is isotropic and density-insensitive, leading to systematically misaligned optimization directions. To address this, we revisit offline RL from a geometric perspective and show that policy refinement can be formulated as a local transport map: an initial flow policy augmented by a residual displacement. By analyzing the induced density transformation, we derive a local quadratic approximation of the KL-constrained objective governed by the Fisher information matrix, enabling a tractable anisotropic optimization formulation. By leveraging the score function embedded in the flow velocity, we obtain a corresponding quadratic constraint for efficient optimization. Our results reveal that the optimality gap in prior methods arises from their isotropic approximation. In contrast, our framework achieves a controllable approximation error within a provable neighborhood of the optimal solution. Extensive experiments demonstrate state-of-the-art performance across diverse offline RL benchmarks. See project page: https://github.com/ARC0127/Fisher-Decorator.

Recursive or looped language models have recently emerged as a new scaling axis by iteratively refining the same model computation over latent states to deepen reasoning. We extend such scaling principle from a single model to multi-agent systems, and ask: Can agent collaboration itself be scaled through recursion? To this end, we introduce RecursiveMAS, a recursive multi-agent framework that casts the entire system as a unified latent-space recursive computation. RecursiveMAS connects heterogeneous agents as a collaboration loop through the lightweight RecursiveLink module, enabling in-distribution latent thoughts generation and cross-agent latent state transfer. To optimize our framework, we develop an inner-outer loop learning algorithm for iterative whole-system co-optimization through shared gradient-based credit assignment across recursion rounds. Theoretical analyses of runtime complexity and learning dynamics establish that RecursiveMAS is more efficient than standard text-based MAS and maintains stable gradients during recursive training. Empirically, we instantiate RecursiveMAS under 4 representative agent collaboration patterns and evaluate across 9 benchmarks spanning mathematics, science, medicine, search, and code generation. In comparison with advanced single/multi-agent and recursive computation baselines, RecursiveMAS consistently delivers an average accuracy improvement of 8.3%, together with 1.2times-2.4times end-to-end inference speedup, and 34.6%-75.6% token usage reduction. Code and Data are provided in https://recursivemas.github.io.

In this work, we investigate the application of Taylor expansions in reinforcement learning. In particular, we propose Taylor expansion policy optimization, a policy optimization formalism that generalizes prior work (e.g., TRPO) as a first-order special case. We also show that Taylor expansions intimately relate to off-policy evaluation. Finally, we show that this new formulation entails modifications which improve the performance of several state-of-the-art distributed algorithms.

Self-reflection is a powerful mechanism for credit assignment in human learning, converting sparse outcome feedback into actionable guidance. However, its potential for post-training Large Language Models (LLMs) remains underexplored. We propose Self-Reflective Policy Optimization (SRPO), a framework that internalizes this capability. SRPO enables LLMs to analyze their own completed trajectories, synthesize errors into concise "reflection patches," and use reflection-conditioned teacher scores on student on-policy rollouts as dense token-level training signals. This process effectively transforms sparse terminal supervision into dense, token-level learning signals without requiring external critics, separate reward models, or larger teacher models. We demonstrate that SRPO achieves state-of-the-art performance across mathematical reasoning and long-horizon agentic benchmarks with exceptional data efficiency. Using a Qwen3-8B base model, SRPO attains 73.3% on AIME'24 using only 8% (0.08x) of the training FLOPs required by scaled supervised fine-tuning, while significantly improving success rates on WebShop (64.7%), ALFWorld (76.8%), and SWE-Bench-Lite (31.2%). Code is available at https://github.com/Galleons2029/SRPO

Recent advances in language model (LM) agents and function calling have enabled autonomous, feedback-driven systems to solve problems across various digital domains. To better understand the unique limitations of LM agents, we introduce RefactorBench, a benchmark consisting of 100 large handcrafted multi-file refactoring tasks in popular open-source repositories. Solving tasks within RefactorBench requires thorough exploration of dependencies across multiple files and strong adherence to relevant instructions. Every task is defined by 3 natural language instructions of varying specificity and is mutually exclusive, allowing for the creation of longer combined tasks on the same repository. Baselines on RefactorBench reveal that current LM agents struggle with simple compositional tasks, solving only 22% of tasks with base instructions, in contrast to a human developer with short time constraints solving 87%. Through trajectory analysis, we identify various unique failure modes of LM agents, and further explore the failure mode of tracking past actions. By adapting a baseline agent to condition on representations of state, we achieve a 43.9% improvement in solving RefactorBench tasks. We further extend our state-aware approach to encompass entire digital environments and outline potential directions for future research. RefactorBench aims to support the study of LM agents by providing a set of real-world, multi-hop tasks within the realm of code.

Group Relative Policy Optimization (GRPO) has become a standard reinforcement learning method for post-training language models. Recent work shows that GRPO can reduce the base model's reasoning capacity and underperform it in Pass@k when k is large, indicating reduced coverage of reasoning paths. We find that this reduction is associated with GRPO concentrating on responses that the base model already generates with high probability. We trace this concentration to two mechanisms in the GRPO update. At the response level, high-probability responses dominate the group gradient through repeated occurrence. At the token level, GRPO's importance ratio scales gradients, further reinforcing tokens that become more likely under the current policy. We propose ReCo, a reweighting method that addresses both effects. Response contributions are normalized by their expected occurrence within the rollout group, and the token-level importance ratio is replaced with a variance-based ratio that gives larger update scale to non-saturated decision points where alternative token choices remain plausible. Across Qwen2.5-Math-1.5B/7B and Llama-3.1-8B-Instruct on five mathematical reasoning benchmarks, ReCo improves Pass@k for large values of k and is comparable to GRPO for small values of k.

Recent advances in LLM agents have largely built on reasoning backbones like ReAct, which interleave thought and action in complex environments. However, ReAct often produces ungrounded or incoherent reasoning steps, leading to misalignment between the agent's actual state and goal. Our analysis finds that this stems from ReAct's inability to maintain consistent internal beliefs and goal alignment, causing compounding errors and hallucinations. To address this, we introduce ReflAct, a novel backbone that shifts reasoning from merely planning next actions to continuously reflecting on the agent's state relative to its goal. By explicitly grounding decisions in states and enforcing ongoing goal alignment, ReflAct dramatically improves strategic reliability. This design delivers substantial empirical gains: ReflAct surpasses ReAct by 27.7% on average, achieving a 93.3% success rate in ALFWorld. Notably, ReflAct even outperforms ReAct with added enhancement modules (e.g., Reflexion, WKM), showing that strengthening the core reasoning backbone is key to reliable agent performance.

A long-standing goal of AI is a model that can continually learn and improve itself. On post-trained models, supervised finetuning (SFT) on new data often causes poor generalization and catastrophic forgetting. As such, the conventional wisdom is that on-policy training is a prerequisite for continual learning. In practice, however, data containing new knowledge or capabilities are often off-policy. While methods such as on-policy self-distillation (OPSD) try to bridge this gap by converting off-policy data into on-policy signal, they have been shown to cause reasoning collapse. In this paper, we show that off-policy merging beats OPSD for continual learning. We first show that SFT learns a useful signal from new data, but naively applying its update interferes with existing capabilities. We reduce this interference with a simple recipe we term grafting, which changes where the update is learned and how it is applied: (1) learning the update on an earlier donor checkpoint, ideally even before the end of pretraining, and applying the weight update to the post-trained model; (2) scaling the weight update, equivalent to a form of model merging; and (3) optionally, masking the most sensitive update directions when the new data distribution is far from the post-trained model. Across continual learning settings including (1) distilling from expert traces, (2) self-improvement with STaR and Pedagogical RL, and (3) injecting knowledge after pretraining cutoff, grafting Pareto-dominates both SFT and OPSD in new-task and old-task performance, while avoiding expensive on-policy sampling. Therefore, our work challenges on-policy training as a necessity for continual learning on RL-trained models.

Large language models (LLM) often hallucinate, and while adding citations is a common solution, it is frequently insufficient for accountability as users struggle to verify how a cited source supports a generated claim. Existing methods are typically coarse-grained and fail to distinguish between direct quotes and complex reasoning. In this paper, we introduce Generation-time Fine-grained Provenance, a task where models must generate fluent answers while simultaneously producing structured, sentence-level provenance triples. To enable this, we present ReFInE (Relation-aware Fine-grained Interpretability & Evidence), a dataset featuring expert verified annotations that distinguish between Quotation, Compression, and Inference. Building on ReFInE, we propose GenProve, a framework that combines Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO). By optimizing a composite reward for answer fidelity and provenance correctness, GenProve significantly outperforms 14 strong LLMs in joint evaluation. Crucially, our analysis uncovers a reasoning gap where models excel at surface-level quotation but struggle significantly with inference-based provenance, suggesting that verifiable reasoning remains a frontier challenge distinct from surface-level citation.

In this paper, we introduce a novel learning paradigm for adaptive Large Language Model (LLM) agents that eliminates the need for fine-tuning the underlying LLMs. Existing approaches are often either rigid, relying on static, handcrafted reflection workflows, or computationally intensive, requiring gradient updates of LLM model parameters. In contrast, our method enables low-cost continual adaptation via memory-based online reinforcement learning. We formalise this as a Memory-augmented Markov Decision Process (M-MDP), equipped with a neural case-selection policy to guide action decisions. Past experiences are stored in an episodic memory, either differentiable or non-parametric. The policy is continually updated based on environmental feedback through a memory rewriting mechanism, whereas policy improvement is achieved through efficient memory reading (retrieval). We instantiate our agent model in the deep research setting, namely AgentFly, which attains top-1 on GAIA validation (87.88% Pass@3) and 79.40% on the test set. It reaches 66.6% F1 and 80.4% PM on the DeepResearcher dataset, outperforming the state-of-the-art training-based method, while case-based memory adds 4.7% to 9.6% absolute points on out-of-distribution tasks. Our approach offers a scalable and efficient pathway for developing generalist LLM agents capable of continuous, real-time learning without gradient updates, advancing machine learning towards open-ended skill acquisition and deep research scenarios. The code is available at https://github.com/Agent-on-the-Fly/AgentFly.

Search-integrated reasoning enables language agents to transcend static parametric knowledge by actively querying external sources. However, training these agents via reinforcement learning is hindered by the multi-scale credit assignment problem: existing methods typically rely on sparse, trajectory-level rewards that fail to distinguish between high-quality reasoning and fortuitous guesses, leading to redundant or misleading search behaviors. To address this, we propose Search-R2, a novel Actor-Refiner collaboration framework that enhances reasoning through targeted intervention, with both components jointly optimized during training. Our approach decomposes the generation process into an Actor, which produces initial reasoning trajectories, and a Meta-Refiner, which selectively diagnoses and repairs flawed steps via a 'cut-and-regenerate' mechanism. To provide fine-grained supervision, we introduce a hybrid reward design that couples outcome correctness with a dense process reward quantifying the information density of retrieved evidence. Theoretically, we formalize the Actor-Refiner interaction as a smoothed mixture policy, proving that selective correction yields strict performance gains over strong baselines. Extensive experiments across various general and multi-hop QA datasets demonstrate that Search-R2 consistently outperforms strong RAG and RL-based baselines across model scales, achieving superior reasoning accuracy with minimal overhead.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central post-training paradigm for improving the reasoning capabilities of large language models. Yet existing methods share a common blind spot: they optimize policies based on instantaneous group-level or batch-level statistics without ever verifying whether the resulting update actually improved the model. This open-loop design -- updating in isolation at each step, guided only by within-group (batch) reward signals -- means optimization can drift or collapse with no mechanism to detect and correct these failures. We argue that the missing ingredient is policy improvement feedback: the ability to measure and optimize inter-iteration progress directly. To this end, we introduce Policy Improvement Reinforcement Learning (PIRL), a framework that replaces surrogate reward maximization with the explicit objective of maximizing cumulative policy improvement across iterations, and prove this temporal objective is perfectly aligned with maximizing final task performance. Building on PIRL, we propose Policy Improvement Policy Optimization (PIPO), which implements closed-loop optimization through retrospective verification. At each iteration, PIPO evaluates whether the previous update yielded genuine improvement against a sliding-window historical baseline, then actively reinforces beneficial updates and suppresses the harmful ones -- transforming an open-loop process into a self-correcting one. We provide theoretical analysis showing that PIPO performs ascent on the PIRL objective in expectation, and experiments on mathematical reasoning benchmarks demonstrate improved stability and performance over GRPO and its variants.

Recent game design agents have made substantial progress in generating playable games. However, program correctness does not ensure an enjoyable experience for players. We present Recursive Game Creator, an experience-oriented harness to advance agentic game development from rough game prototypes into entertaining games. Recursive Game Creator organizes recursive development around four components: Designer, Builder, Player, and Reviewer. The Designer translates user instructions and Reviewer's feedback into detailed plans. The Builder turns these plans into candidate games. The coding-native Player creates and executes reusable policies through programmatic interfaces to efficiently collect diverse gameplay trajectories, mitigating evaluation bias caused by slow GUI-based collection. The Reviewer uses carefully designed trajectory-based metrics to induce player preferences, integrating with visual evidence and explicit textual preferences to evaluate games against game-specific criteria. Finally, the Reviewer accepts the better version and provides improvement reviews for the next round, closing the recursive loop. Our method achieves state-of-the-art overall performance of 77.89 on GameCraft-Bench. On GameASG-Bench, it achieves a strict task success rate of 53.2%, a 34.1% improvement over the same-model baseline, and the highest mean runtime-check pass rate at 93.4% among compared methods. A user study shows longer playtime and higher ratings. Code is coming soon.

Group Relative Policy Optimization (GRPO) was introduced and used recently for promoting reasoning in LLMs under verifiable (binary) rewards. We show that the mean + variance calibration of these rewards induces a weighted contrastive loss in which the contrastive samples are synthetic data drawn from the previous policy. While GRPO was originally paired with clipping to keep updates near the old policy, we analyze variants that differ in reward normalization (mean-only vs mean + variance) and in how they regularize updates using KL divergence: either penalizing divergence from the previous model (mirror), penalizing divergence from a fixed reference model π_{ref}, or combining both forms of regularization. For each, the optimal policy π_n admits an explicit form in terms of the binary reward and the first and second order statistics of the reward under π_{n-1}, as well as the policies π_{n-1} and π_{ref}. Iterating results in a sequence {π_n} whose probability of success (PoS) obeys a simple recurrence that converges to a fixed point determined by the reference PoS and the regularization strength. We further show that this fixed point exceeds the reference, demonstrating that GRPO amplifies the policy's probability of success.

Reinforcement learning (RL) is vital for optimizing large language models (LLMs). Recent Group Relative Policy Optimization (GRPO) estimates advantages using multiple on-policy outputs per prompt, leading to high computational costs and low data efficiency. To address this, we introduce Replay-Enhanced Policy Optimization (RePO), which leverages diverse replay strategies to retrieve off-policy samples from a replay buffer, allowing policy optimization based on a broader and more diverse set of samples for each prompt. Experiments on five LLMs across seven mathematical reasoning benchmarks demonstrate that RePO achieves absolute average performance gains of 18.4 and 4.1 points for Qwen2.5-Math-1.5B and Qwen3-1.7B, respectively, compared to GRPO. Further analysis indicates that RePO increases computational cost by 15% while raising the number of effective optimization steps by 48% for Qwen3-1.7B, with both on-policy and off-policy sample numbers set to 8. The repository can be accessed at https://github.com/SihengLi99/RePO.

Interactive language-model agents increasingly solve complex tasks through long-horizon, multi-call reasoning, where errors in beliefs or actions can compound across tool interactions. Retrospective search can recover from such failures but is prone to misallocation. Delayed outcomes obscure the contribution of intermediate search decisions, leading to Attribution Complexity, while evolving execution evidence leads to Adaptation Complexity, where previously learned estimates become stale. To address these challenges, we first introduce Search Value Dynamics (SVD), which characterizes the evolving trade-off between the gain and cost of retrospective search. Building on SVD, we propose ForkPilot, a self-evolving two-stage policy-learning framework. In the first stage, ForkPilot learns a search-value policy offline from completed trajectories through automatically constructed outcome comparisons. In the second stage, it makes search decisions based on current observations and then self-evolves by incorporating newly completed trajectories into subsequent policy updates. We evaluate ForkPilot across 6 diverse benchmarks and 7 widely used LLM backbone families, including four open-source families, GPT-5.6 Sol, and Opus 4.8 in a production agentic system, against 9 competitive baselines, including a real-world harness deployment used by hundreds of thousands of paid users. ForkPilot achieves comparable state-of-the-art performance while reducing token usage by up to 59.2%, demonstrating its efficacy.

An LLM agent's capability is largely magnified by its harness, namely the prompts, control flow, tooling, memory, and context management surrounding the frozen backbone model. Recent methods increasingly automate this process by iteratively proposing and selecting component-wise edits of an agent harness, practically establishing a form of recursive self-improvement (RSI) at the agent-system level. However, such recursive evolution may overfit by memorizing the training tasks, showing large in-distribution gains that shrink or even vanish on out-of-distribution benchmarks. We introduce Regularized Recursive Self-Improvement of Agent Harnesses (RRSI), which incorporates the principles of regularizations into harness self-improvement by constraining the evolution candidate proposal and selection. The proposer operates with a temporally annealed budget, limiting how many edits a candidate can bundle, and it encourages unexplored trajectories based on evolution history. The selector is equipped with a critic and a pruner: the critic screens benchmark-specific proposals, while the pruner, removes changes that are too small, too expensive, or no longer useful. Together these constraints favor reusable agent mechanisms over benchmark-specific ones or even noises. Across eight benchmarks spanning coding, agentic workspace and engineering design tasks, RRSI gains up to 14.1 points on the split it evolves against and up to 4.7 points on the five out-of-distribution benchmarks, while producing a harness that runs on 30% fewer policy tokens than the unregularized evolution. Code is available at https://github.com/google-research/rrsi and project page is https://regularized-rsi.com/.

Reinforcement learning (RL) has become central to enhancing reasoning in large language models (LLMs). Yet on-policy algorithms such as Group Relative Policy Optimization (GRPO) often suffer in early training: noisy gradients from low-quality rollouts lead to unstable updates and inefficient exploration. We introduce Slow-Fast Policy Optimization (SFPO), a simple yet efficient framework to address these limitations via decomposing each step into three stages: a short fast trajectory of inner steps on the same batch, a reposition mechanism to control off-policy drift, and a final slow correction. This reposition-before-update design preserves the objective and rollout process unchanged, making SFPO plug-compatible with existing policy-gradient pipelines. Extensive experiments demonstrate that SFPO consistently improves stability, reduces rollouts, and accelerates convergence of reasoning RL training. Specifically, it outperforms GRPO by up to 2.80 points in average on math reasoning benchmarks. It also achieves up to 4.93 fewer rollouts and a 4.19 reduction in wall-clock time to match GRPO's best accuracy.

Large language models (LLMs) typically receive diverse natural language (NL) feedback through interaction with the environment. However, current reinforcement learning (RL) algorithms rely solely on scalar rewards, leaving the rich information in NL feedback underutilized and leading to inefficient exploration. In this work, we propose GOLF, an RL framework that explicitly exploits group-level language feedback to guide targeted exploration through actionable refinements. GOLF aggregates two complementary feedback sources: (i) external critiques that pinpoint errors or propose targeted fixes, and (ii) intra-group attempts that supply alternative partial ideas and diverse failure patterns. These group-level feedbacks are aggregated to produce high-quality refinements, which are adaptively injected into training as off-policy scaffolds to provide targeted guidance in sparse-reward regions. Meanwhile, GOLF jointly optimizes generation and refinement within a unified RL loop, creating a virtuous cycle that continuously improves both capabilities. Experiments on both verifiable and non-verifiable benchmarks show that GOLF achieves superior performance and exploration efficiency, achieving 2.2times improvements in sample efficiency compared to RL methods trained solely on scalar rewards. Code is available at https://github.com/LuckyyySTA/GOLF.

Document repositories evolve continuously. Guidelines and policies are revised, superseded, and re-uploaded, so the same content recurs in different wording and newer versions refine or contradict earlier ones. These inconsistencies belong to the growing collection rather than to any single document, yet existing work treats versioning, duplicate detection, and contradiction detection as isolated pairwise tasks and stops once a pair is labeled. We present GVD (Governed Versioning and Deduplication), a framework that unifies cross-document version linking with rule-level conflict resolution under an auditable update policy. Incoming documents are assigned to version families through bidirectional rule alignment, and their rules are compared against the family memory to identify duplicates, contradictions, asymmetric refinements, and new knowledge, with Counterfactual Span Probing (CSP) resolving related pairs that inference misclassifies as neutral. Relation-specific policies suppress duplicates and escalate only consequential changes for review, retaining version lineage as an audit trail. The pipeline runs fully locally, with no large language model. On 120 enterprise documents processed as 140 ingestions across 59 version families, GVD reaches an F1 of 0.97 for version-family construction and 0.94 for rule-level consistency, with CSP raising rule consistency from 0.90 to 0.94.

Automated source code refactoring, particularly extract method refactoring, is a crucial and frequently employed technique during software development. Despite its importance and frequent use by practitioners, current automated techniques face significant limitations. These approaches often rely on developers to identify the precise bounds of refactoring opportunities in terms of source code statements. Also, they often do not capture the semantic context, resulting in offering no automated means to suggest meaningful method name, for instance. To address these challenges, we propose a novel reinforcement learning-based approach for fine-tuning and aligning code language models to perform automated, intelligent extract method refactoring on Java source code. Our approach fine-tunes sequence-to-sequence generative models and aligns them using the Proximal Policy Optimization (PPO) algorithm. We utilize code compilation and presence of the refactoring in the generated code as reward signals, providing a code-centric optimization process. Our experiments demonstrate that our approach significantly enhances the performance of large language models in code refactoring, as evidenced by both quantitative evaluation metrics such as BLEU, ROUGE, and CodeBLEU, and qualitative measures including syntactical and functional correctness. The supervised fine-tuned model, further aligned with PPO, surpasses traditional supervised fine-tuning by 11.96% and 16.45% in terms of BLEU and CodeBLEU scores, respectively. When subjected to a suite of 122 unit tests, the number of successful tests increased from 41 to 66 for the reinforcement learning aligned fine-tuned Code-T5 model, highlighting the effectiveness of our approach in producing functionally correct refactorings.

Optimizing deployed AI systems increasingly amounts to editing prompts, skills, harnesses, and code rather than model weights. Existing approaches commonly optimize these artifacts through propose-evaluate-select procedures, where candidate configurations are evaluated and only those meeting an acceptance criterion are selected. Yet our analysis shows that discarded candidates often contain information critical for subsequent optimization. Discarding them causes later proposals to revisit the same failure modes. We introduce Mara Chain, a refinement procedure that turns rejected candidates into stepping stones. Rather than discarding a rejected candidate, Mara Chain retains and iteratively refines it using evidence accumulated across preceding attempts. The procedure limits each refinement chain to a fixed depth and applies Pareto-filtered Top-N selection to bound the candidate pool. Across AppWorld skill optimization, TerminalBench 2.1 harness optimization, and MuSiQue retrieval-pipeline optimization, Mara Chain delivers greater task-performance gains with fewer rollouts. It outperforms GEPA, ACE, and SkillOpt-Lite by up to 20.5% in relative performance on AppWorld, reaching the target score with 65.5% fewer rollouts than GEPA. It improves the pass rate by 20.2 and 22.5 percentage points over AHE and Meta-Harness on TerminalBench 2.1, respectively, and improves MuSiQue test nDCG@10 and Recall@10 by 0.104 and 0.131 over a hand-written retrieval pipeline.

Large language model (LLM) agents are increasingly used for complex tasks, yet deployed agents often remain static, failing to adapt as user needs evolve. This creates a tension between the need for continuous service and the necessity of updating capabilities to match shifting task distributions. On platforms like OpenClaw, which handle diverse workloads across 20+ channels, existing methods either store raw trajectories without distilling knowledge, maintain static skill libraries, or require disruptive downtime for retraining. We present MetaClaw, a continual meta-learning framework that jointly evolves a base LLM policy and a library of reusable behavioral skills. MetaClaw employs two complementary mechanisms. Skill-driven fast adaptation analyzes failure trajectories via an LLM evolver to synthesize new skills, enabling immediate improvement with zero downtime. Opportunistic policy optimization performs gradient-based updates via cloud LoRA fine-tuning and Reinforcement Learning with a Process Reward Model (RL-PRM). This is triggered during user-inactive windows by the Opportunistic Meta-Learning Scheduler (OMLS), which monitors system inactivity and calendar data. These mechanisms are mutually reinforcing: a refined policy generates better trajectories for skill synthesis, while richer skills provide higher-quality data for policy optimization. To prevent data contamination, a versioning mechanism separates support and query data. Built on a proxy-based architecture, MetaClaw scales to production-size LLMs without local GPUs. Experiments on MetaClaw-Bench and AutoResearchClaw show that skill-driven adaptation improves accuracy by up to 32% relative. The full pipeline advances Kimi-K2.5 accuracy from 21.4% to 40.6% and increases composite robustness by 18.3%. Code is available at https://github.com/aiming-lab/MetaClaw.

Recent advances in multi-agent reinforcement learning, particularly Policy-Space Response Oracles (PSRO), have enabled the computation of approximate game-theoretic equilibria in increasingly complex domains. However, these methods rely on deep reinforcement learning oracles that produce `black-box' neural network policies, making them difficult to interpret, trust or debug. We introduce Code-Space Response Oracles (CSRO), a novel framework that addresses this challenge by replacing RL oracles with Large Language Models (LLMs). CSRO reframes the best response computation as a code generation task, prompting an LLM to generate policies directly as human-readable code. This approach not only yields inherently interpretable policies but also leverages the LLM's pretrained knowledge to discover complex, human-like strategies. We explore multiple ways to construct and enhance an LLM-based oracle: zero-shot prompting, iterative refinement and AlphaEvolve, a distributed LLM-based evolutionary system. We demonstrate that CSRO achieves performance competitive with baselines while producing a diverse set of explainable policies. Our work presents a new perspective on multi-agent learning, shifting the focus from optimizing opaque policy parameters to synthesizing interpretable algorithmic behavior.

We introduce and release ScienceBuddy, an interactive scientific research workspace that brings continually improving scientific agents into researchers' everyday workflows. ScienceBuddy supports researchers in carrying out scientific tasks while transforming their requests, feedback, and execution evidence into tasks and evaluation rubrics for continual learning. At its core is recursive-in-recursive self-improvement, a paradigm that couples harness evolution with model reinforcement learning: the inner recursion improves the harness with the model fixed, while the outer recursion trains the model under the improved harness. Harness evolution shapes training experience, and model learning creates new opportunities for harness adaptation. We present case studies of researcher interaction, harness refinement, and model learning, with the benchmark cases spanning four scientific task families. By releasing ScienceBuddy as a research product, we make this paradigm available to the scientific community and take a step toward discovery intelligence: scientific AI that advances through sustained collaboration with researchers and evolves alongside the research it supports. Website: http://science-buddy.io

Modern conversational agents like ChatGPT and Alexa+ rely on predefined policies specifying metadata, response styles, and tool-usage rules. As these LLM-based systems expand to support diverse business and user queries, such policies, often implemented as in-context prompts, are becoming increasingly complex and lengthy, making faithful adherence difficult and imposing large fixed computational costs. With the rise of multimodal agents, policies that govern visual and multimodal behaviors are critical but remain understudied. Prior prompt-compression work mainly shortens task templates and demonstrations, while existing policy-alignment studies focus only on text-based safety rules. We introduce Multimodal Policy Internalization (MPI), a new task that internalizes reasoning-intensive multimodal policies into model parameters, enabling stronger policy-following without including the policy during inference. MPI poses unique data and algorithmic challenges. We build two datasets spanning synthetic and real-world decision-making and tool-using tasks and propose TriMPI, a three-stage training framework. TriMPI first injects policy knowledge via continual pretraining, then performs supervised finetuning, and finally applies PolicyRollout, a GRPO-style reinforcement learning extension that augments rollouts with policy-aware responses for grounded exploration. TriMPI achieves notable gains in end-to-end accuracy, generalization, and robustness to forgetting. As the first work on multimodal policy internalization, we provide datasets, training recipes, and comprehensive evaluations to foster future research. Project page: https://mikewangwzhl.github.io/TriMPI.

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

Tool-integrated reasoning (TIR) enables LLM agents to solve tasks through planning, tool use, and iterative revision, but outcome-only reinforcement learning in this setting suffers from sparse, delayed rewards and weak step-level credit assignment. In long-horizon TIR trajectories, an early irrecoverable mistake can determine success or failure, making it crucial to localize the first irrecoverable step and leverage it for fine-grained credit assignment. We propose Error-Localized Policy Optimization (ELPO), which localizes the first irrecoverable step via binary-search rollout trees under a fixed rollout budget, converts the resulting tree into stable learning signals through hierarchical advantage attribution, and applies error-localized adaptive clipping to strengthen corrective updates on the critical step and its suffix. Across TIR benchmarks in math, science QA, and code execution, ELPO consistently outperforms strong Agentic RL baselines under comparable sampling budgets, with additional gains in Pass@K and Major@K scaling, rollout ranking quality, and tool-call efficiency. Our code will be publicly released soon.

Group Relative Policy Optimization (GRPO) improves language-model reasoning by comparing verified rewards among multiple solution rollouts for each query. However, difficult training queries can yield only incorrect rollouts, leaving GRPO with no reward contrast or learning signal. Prior hint-based methods construct auxiliary hints from solution evidence and use them to re-solve failed queries, recovering learning signal. Yet the resulting trajectories are typically treated as ordinary solution trajectories despite being generated under an assisted condition unavailable at evaluation. We discover hinted reward shift: recovered reward contrast can concentrate policy updates on hinted trajectories, limiting improvement without hints. This also creates a trade-off: increasing hinted trajectories can accelerate early learning but intensify reward shift later. To address this problem, we propose HATCH (Hint-Annealed Self-Teaching), an online single-policy framework that learns from both generating and using its own hints to improve reasoning without assistance. To mitigate hinted reward shift, we introduce online weighting to anneal the contribution of hinted trajectories. However, learning to generate hints can conflict with improving query solving. We therefore use gradient projection to remove the opposing component of hint-generation updates. Together, these designs support self-improvement by enabling the policy to create learning opportunities for itself and turn them into stronger reasoning without hints. We evaluate our method on mathematical reasoning benchmarks and outperform state-of-the-art methods by 1.02 pp on Llama-3.2-1B-Instruct, 2.84 pp on Qwen3-1.7B, and 4.32 pp on Qwen3-8B.

A central paradox in fine-tuning Large Language Models (LLMs) with Reinforcement Learning with Verifiable Reward (RLVR) is the frequent degradation of multi-attempt performance (Pass@k) despite improvements in single-attempt accuracy (Pass@1). This is often accompanied by catastrophic forgetting, where models lose previously acquired skills. While various methods have been proposed, the choice and function of the divergence term have been surprisingly unexamined as a proactive solution. We argue that standard RLVR objectives -- both those using the mode-seeking reverse KL-divergence and those forgoing a divergence term entirely -- lack a crucial mechanism for knowledge retention. The reverse-KL actively accelerates this decay by narrowing the policy, while its absence provides no safeguard against the model drifting from its diverse knowledge base. We propose a fundamental shift in perspective: using the divergence term itself as the solution. Our framework, Diversity-Preserving Hybrid RL (DPH-RL), leverages mass-covering f-divergences (like forward-KL and JS-divergence) to function as a rehearsal mechanism. By continuously referencing the initial policy, this approach forces the model to maintain broad solution coverage. Extensive experiments on math and SQL generation demonstrate that DPH-RL not only resolves the Pass@k degradation but improves both Pass@1 and Pass@k in- and out-of-domain. Additionally, DPH-RL is more training-efficient because it computes f-divergence using generator functions, requiring only sampling from the initial policy and no online reference model. Our work highlights a crucial, overlooked axis for improving RLVR, demonstrating that the proper selection of a divergence measure is a powerful tool for building more general and diverse reasoning models.

Recent focus in agentic reinforcement learning (RL) seeks to improve credit assignment in long-horizon tasks. One promising direction combines reinforcement learning with verifiable rewards (RLVR) and on-policy self-distillation (OPSD), integrating trajectory-level advantages with dense token-level supervision. This line of work often conditions a teacher model on privileged context, such as agentic skills, to score tokens generated by the student policy. Despite their progress, they largely overlook the on-policy evolution of agentic skills and the reliability of teacher supervision. Towards this end, we introduce Recursive Self-Improving Policy Optimization (RSIPO), a self-evolving agentic RL framework that enables agentic skills and the policy model to co-evolve throughout the training process. Specifically, RSIPO enables the policy itself to extract skills from completed trajectories and explicitly optimizes its skill-generation capability through trajectory replay. It further employs empirical Bayes shrinkage to dynamically calibrate the student's trust in teacher scores, accounting for the fact that skill-enhanced teacher guidance can sometimes be less reliable. Experiments with Qwen-family models on embodied interaction and search-based agentic tasks demonstrate that RSIPO outperforms all the compared baseline approaches. With Qwen2.5-7B as the base model, RSIPO achieves an average success rate of 98.6\% on ALFWorld, yielding absolute improvements of 2.5\% and 17.4\% over the second-best baseline and standard GRPO, respectively.

Post-training has become central to turning pretrained large language models (LLMs) into aligned, capable, and deployable systems. Recent progress spans supervised fine-tuning (SFT), preference optimization, reinforcement learning (RL), process supervision, verifier-guided methods, distillation, and multi-stage pipelines. Yet these methods are often discussed in fragmented ways, organized by labels or objectives rather than by the behavioral bottlenecks they address. This survey argues that LLM post-training is best understood as structured intervention on model behavior. We organize the field first by trajectory provenance, which defines two primary regimes: off-policy learning on externally supplied trajectories and on-policy learning on learner-generated rollouts. We then interpret methods through two recurring roles -- effective support expansion, which makes useful behaviors more reachable, and policy reshaping, which improves behavior within already reachable regions -- together with a complementary systems-level role, behavioral consolidation, which preserves, transfers, and amortizes useful behavior across stages and model transitions. Under this view, SFT may serve either support expansion or policy reshaping; preference optimization is usually off-policy reshaping, though online variants move closer to learner-generated states. On-policy RL often improves behavior on learner-generated states, but stronger guidance can also make hard-to-reach reasoning paths reachable. Distillation is often better understood as consolidation rather than only compression, and hybrid pipelines emerge as coordinated multi-stage compositions. Overall, the framework helps diagnose post-training bottlenecks and reason about stage composition, suggesting that progress increasingly depends on coordinated systems design rather than any single dominant objective.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models. However, rollout-intensive policy optimization is often limited by insufficient reward contrast, arising when overly simple or complex prompts generate low-variance feedback and when outcome-only rewards assign the same terminal assessment to every decision in a multi-turn rollout. Past efforts have focused on allocating available rollout resources to promising prompts, yet they only leverage sample informativeness at the prompt level and neglect variation in prefix-level informativeness across turns within the same rollout. This work targets multi-turn agentic RL by modeling each ReAct-style thought-action-observation turn as a semantically distinct node, allowing budget allocation to extend from prompt roots to turn-level prefixes with further continuations, which naturally forms tree-structured rollouts. We introduce Tree Rollout Allocation for Contrastive Exploration (TRACE), a unified rollout allocation framework that enhances reward contrast within a fixed sampling budget. Technically, TRACE allocates rollout budget to both prompt roots and intermediate prefixes that are most likely to yield mixed terminal rewards. A shared generalizable predictor estimates conditional success probability at these anchors from prefix histories to guide this allocation. The resulting adaptive tree structure enriches outcome-only feedback and amplifies the policy-update signal. Empirically, TRACE achieves competitive performance and efficiency gains on typical agentic benchmarks, e.g., improving Qwen3-14B Multi-Hop QA average accuracy by 2.8 points over competitive baselines at equal sampling cost.

Self-improving LLM agents refine answers, not the process that produces those answers. Systems that add a meta-level hold that level fixed, and those that edit themselves must leave part of their own editing machinery untouched to stay stable, capping the meta-depth they realize at roughly two. We present Meta^n, which keeps the meta-operation fixed and recurses on its input instead. That operation, Ω, is applied repeatedly to its own products, reading the traces of the solver stack below together with the code that produced them, then writing the next layer as a strategic pre-process and a library of callable helpers. Because Ω never changes, it cannot destabilize the system, and because its input strictly grows, each layer reasons from a higher vantage than the last. Depth is set by convergence rather than fixed in advance, and an evolutionary archive searches over layer chains. Across two backbones, Meta^n outperforms prior self-improving agents on all eight benchmark families. The sharpest case is ARC-AGI-2, built to resist skill memorization, where it alone scores above zero. Ablations indicate that most of the gain from recursion comes from the conditioning each layer passes to the next, and distinct layer roles emerge with depth although no prompt prescribes them. Code available at https://github.com/minnesotanlp/meta-n

Large Language Models (LLMs) exhibit robust problem-solving capabilities for diverse tasks. However, most LLM-based agents are designed as specific task solvers with sophisticated prompt engineering, rather than agents capable of learning and evolving through interactions. These task solvers necessitate manually crafted prompts to inform task rules and regulate LLM behaviors, inherently incapacitating to address complex dynamic scenarios e.g., large interactive games. In light of this, we propose Agent-Pro: an LLM-based Agent with Policy-level Reflection and Optimization that can learn a wealth of expertise from interactive experiences and progressively elevate its behavioral policy. Specifically, it involves a dynamic belief generation and reflection process for policy evolution. Rather than action-level reflection, Agent-Pro iteratively reflects on past trajectories and beliefs, fine-tuning its irrational beliefs for a better policy. Moreover, a depth-first search is employed for policy optimization, ensuring continual enhancement in policy payoffs. Agent-Pro is evaluated across two games: Blackjack and Texas Hold'em, outperforming vanilla LLM and specialized models. Our results show Agent-Pro can learn and evolve in complex and dynamic scenes, which also benefits numerous LLM-based applications.

This paper introduces Personalized Path Recourse, a novel method that generates recourse paths for an agent. The objective is to achieve desired goals (e.g., better outcomes compared to the agent's original paths of action), while ensuring a high similarity to the agent's original paths and being personalized to the agent. Personalization refers to the extent to which the new path is tailored to the agent's observed behavior patterns from their policy function. We train a personalized recourse agent to generate such personalized paths, which are obtained using reward functions that consider the goal, similarity, and personalization. The proposed method is applicable to both reinforcement learning and supervised learning settings for correcting or improving sequences of actions or sequences of data to achieve a pre-determined goal. The method is evaluated in various settings and demonstrates promising results.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

In the endeavor to make autonomous robots take actions, task planning is a major challenge that requires translating high-level task descriptions into long-horizon action sequences. Despite recent advances in language model agents, they remain prone to planning errors and limited in their ability to plan ahead. To address these limitations in robotic planning, we advocate a self-refining scheme that iteratively refines a draft plan until an equilibrium is reached. Remarkably, this process can be optimized end-to-end from an analytical perspective without the need to curate additional verifiers or reward models, allowing us to train self-refining planners in a simple supervised learning fashion. Meanwhile, a nested equilibrium sequence modeling procedure is devised for efficient closed-loop planning that incorporates useful feedback from the environment (or an internal world model). Our method is evaluated on the VirtualHome-Env benchmark, showing advanced performance with better scaling for inference computation. Code is available at https://github.com/Singularity0104/equilibrium-planner.

Test-Time Learning (TTL) enables language agents to iteratively refine their performance through repeated interactions with the environment at inference time. At the core of TTL is an adaptation policy that updates the actor policy based on experience from previous episodes, thereby improving future behavior. Existing methods rely on fixed, hand-crafted adaptation policies rather than optimizing them for downstream improvement. We argue that optimal adaptation policies should be learned from task environments, not hand-engineered based on human intuition. To achieve this, we introduce Meta-TTL, a framework that formulates the discovery of effective adaptation policies as a bi-level optimization problem. Within this framework, the inner loop executes the standard TTL process, measuring how effectively a candidate adaptation policy helps an agent correct errors across sequential episodes. Guided by the agent's performance, the outer loop employs evolutionary search over a diverse distribution of training tasks to iteratively refine the adaptation policy. We evaluate Meta-TTL on Jericho and WebArena-Lite across both in-distribution (ID) and out-of-distribution (OOD) settings, using multiple meta-agent backbones. Results on both benchmarks show that Meta-TTL consistently outperforms hand-crafted baselines, suggesting that the optimized adaptation policy encodes transferable strategies that generalize beyond the training task distribution.

Modern language models reason within bounded context, an inherent constraint that poses a fundamental barrier to long-horizon reasoning. We identify recursion as a core principle for overcoming this barrier, and propose recursive models as a minimal realization, where the model can recursively invoke itself to solve subtasks in isolated contexts. We prove that any computable problem admits a recursive decomposition in which each subtask requires only exponentially smaller active context than standard autoregressive models; this strictly surpasses any context management approach confined to a single sequence, such as summarization. We further generalize our framework to modern agentic systems with arbitrary context processing and control flows, and prove that recursive models can achieve optimal power within this broader class. Experimentally, we train a 3B model to reason recursively and evaluate on Boolean satisfiability, a task requiring long-horizon combinatorial search, where it significantly outperforms frontier LLMs.

Group Relative Policy Optimization (GRPO) has been a key driver of recent progress in reinforcement learning with verifiable rewards (RLVR) for large language models, but it is typically trained in a low-staleness, near-on-policy regime that incurs substantial system overhead. We ask a simple question: How off-policy can GRPO be? We show that GRPO-style algorithms can tolerate substantially larger rollout staleness than previously assumed, and propose Mu-GRPO, an RL training framework that organizes training into a small number (e.g., four) of large sequential generation-optimization stages. This design induces high rollout staleness while greatly reducing rollout-optimization switching overhead. To stabilize learning under stale data, Mu-GRPO combines relaxed clipping, which preserves useful stale-rollout gradients, with negative-advantage veto, which removes destabilizing post-trigger suffix updates in negative-advantage responses. Across five language models and multiple math reasoning benchmarks, Mu-GRPO matches or exceeds the performance of standard GRPO while achieving around 2x speedup in wall-clock training time, establishing a substantially improved performance-efficiency trade-off for LLM reinforcement learning.

Training prompts in online reinforcement learning (RL) differ substantially in how informative they are for the current policy: some are already saturated while others are too difficult to yield reliable learning signals, yet both receive equal rollout budget under standard training. We propose an exploration-guided prompt scaffolding framework that adapts the training prompt distribution dynamically throughout RL post-training of multimodal large language models (MLLMs). Central to our approach is the Exploration Potential Score (EPS), a lightweight rollout-based proxy for prompt utility derived from KL-regularized policy improvement theory, computable directly from on-policy rollout statistics without additional overhead. Rather than discarding low-utility prompts, we use a teacher model to generate scaffolded rewrites that preserve the original task intent while making subsequent training more informative, reframing teacher supervision as training-data refinement rather than output imitation. Integrated with GRPO on Geo3K and MMK12, our method consistently outperforms the baseline on both in-domain and out-of-distribution benchmarks, achieving up to 9.7\% relative improvement in-domain and gains of 11.5\% on MathVision and 11.1\% on MMMU-Pro.

Multimodal Large Language Models (MLLMs) have recently demonstrated promising capabilities in multimodal coding tasks such as chart-to-code generation. However, existing methods primarily rely on supervised fine-tuning (SFT), which requires the model to learn code patterns through chart-code pairs but does not expose the model to a code execution environment. Moreover, while self-correction through execution feedback offers a potential route to improve coding quality, even state-of-the-art MLLMs have been shown to struggle with effective self-correction. In this work, we introduce MM-ReCoder, a chart-to-code generation model trained with reinforcement learning (RL) and equipped with self-correction ability. We propose a two-stage multi-turn self-correction RL strategy based on Group Relative Policy Optimization (GRPO). The first stage enhances the model's self-correction ability via rolling out a shared first turn, while the second stage improves the coding capability with full-trajectory optimization. MM-ReCoder learns to produce more accurate and executable code through the interaction with the environment and by iteratively correcting its own outputs. Our results on three chart-to-code benchmarks demonstrate the state-of-the-art performance of MM-ReCoder.

Temporal-difference (TD) methods learn state and action values efficiently by bootstrapping from their own future value predictions, but such a self-bootstrapping mechanism is prone to bootstrapping bias, where the errors in the value targets accumulate across steps and result in biased value estimates. Recent work has proposed to use chunked critics, which estimate the value of short action sequences ("chunks") rather than individual actions, speeding up value backup. However, extracting policies from chunked critics is challenging: policies must output the entire action chunk open-loop, which can be sub-optimal for environments that require policy reactivity and also challenging to model especially when the chunk length grows. Our key insight is to decouple the chunk length of the critic from that of the policy, allowing the policy to operate over shorter action chunks. We propose a novel algorithm that achieves this by optimizing the policy against a distilled critic for partial action chunks, constructed by optimistically backing up from the original chunked critic to approximate the maximum value achievable when a partial action chunk is extended to a complete one. This design retains the benefits of multi-step value propagation while sidestepping both the open-loop sub-optimality and the difficulty of learning action chunking policies for long action chunks. We evaluate our method on challenging, long-horizon offline goal-conditioned tasks and show that it reliably outperforms prior methods. Code: github.com/ColinQiyangLi/dqc.

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

Robust Markov decision processes (RMDPs) provide a promising framework for computing reliable policies in the face of model errors. Many successful reinforcement learning algorithms build on variations of policy-gradient methods, but adapting these methods to RMDPs has been challenging. As a result, the applicability of RMDPs to large, practical domains remains limited. This paper proposes a new Double-Loop Robust Policy Gradient (DRPG), the first generic policy gradient method for RMDPs. In contrast with prior robust policy gradient algorithms, DRPG monotonically reduces approximation errors to guarantee convergence to a globally optimal policy in tabular RMDPs. We introduce a novel parametric transition kernel and solve the inner loop robust policy via a gradient-based method. Finally, our numerical results demonstrate the utility of our new algorithm and confirm its global convergence properties.

As Reinforcement Learning (RL) agents are increasingly employed in diverse decision-making problems using reward preferences, it becomes important to ensure that policies learned by these frameworks in mapping observations to a probability distribution of the possible actions are explainable. However, there is little to no work in the systematic understanding of these complex policies in a contrastive manner, i.e., what minimal changes to the policy would improve/worsen its performance to a desired level. In this work, we present COUNTERPOL, the first framework to analyze RL policies using counterfactual explanations in the form of minimal changes to the policy that lead to the desired outcome. We do so by incorporating counterfactuals in supervised learning in RL with the target outcome regulated using desired return. We establish a theoretical connection between Counterpol and widely used trust region-based policy optimization methods in RL. Extensive empirical analysis shows the efficacy of COUNTERPOL in generating explanations for (un)learning skills while keeping close to the original policy. Our results on five different RL environments with diverse state and action spaces demonstrate the utility of counterfactual explanations, paving the way for new frontiers in designing and developing counterfactual policies.

Humans routinely rely on memory to perform tasks, yet most robot policies lack this capability; our goal is to endow robot policies with the same ability. Naively conditioning on long observation histories is computationally expensive and brittle under covariate shift, while indiscriminate subsampling of history leads to irrelevant or redundant information. We propose a hierarchical policy framework, where the high-level policy is trained to select and track previous relevant keyframes from its experience. The high-level policy uses selected keyframes and the most recent frames when generating text instructions for a low-level policy to execute. This design is compatible with existing vision-language-action (VLA) models and enables the system to efficiently reason over long-horizon dependencies. In our experiments, we finetune Qwen2.5-VL-7B-Instruct and π_{0.5} as the high-level and low-level policies respectively, using demonstrations supplemented with minimal language annotations. Our approach, MemER, outperforms prior methods on three real-world long-horizon robotic manipulation tasks that require minutes of memory. Videos and code can be found at https://jen-pan.github.io/memer/.

Recently, test-time scaling has garnered significant attention from the research community, largely due to the substantial advancements of the o1 model released by OpenAI. By allocating more computational resources during the inference phase, large language models~(LLMs) can extensively explore the solution space by generating more thought tokens or diverse solutions, thereby producing more accurate responses. However, developing an o1-like reasoning approach is challenging, and researchers have been making various attempts to advance this open area of research. In this paper, we present a preliminary exploration into enhancing the reasoning abilities of LLMs through reward-guided tree search algorithms. This framework is implemented by integrating the policy model, reward model, and search algorithm. It is primarily constructed around a tree search algorithm, where the policy model navigates a dynamically expanding tree guided by a specially trained reward model. We thoroughly explore various design considerations necessary for implementing this framework and provide a detailed report of the technical aspects. To assess the effectiveness of our approach, we focus on mathematical reasoning tasks and conduct extensive evaluations on four challenging datasets, significantly enhancing the reasoning abilities of LLMs.

Large language models (LLMs) have demonstrated strong capabilities in translating natural language questions about relational databases into SQL queries. In particular, test-time scaling techniques such as Self-Consistency and Self-Correction can enhance SQL generation accuracy by increasing computational effort during inference. However, these methods have notable limitations: Self-Consistency may select suboptimal outputs despite majority votes, while Self-Correction typically addresses only syntactic errors. To leverage the strengths of both approaches, we propose CSC-SQL, a novel method that integrates Self-Consistency and Self-Correction. CSC-SQL selects the two most frequently occurring outputs from parallel sampling and feeds them into a merge revision model for correction. Additionally, we employ the Group Relative Policy Optimization (GRPO) algorithm to fine-tune both the SQL generation and revision models via reinforcement learning, significantly enhancing output quality. Experimental results confirm the effectiveness and generalizability of CSC-SQL. On the BIRD development set, our 3B model achieves 65.28% execution accuracy, while the 7B model achieves 69.19%. The code will be open sourced at https://github.com/CycloneBoy/csc_sql.

Hard symbolic-reasoning tasks such as Sudoku, maze pathfinding, and ARC remain challenging for LLMs due to their fixed-depth autoregressive reasoning, which limits systematic search, refinement, and backtracking. While recursive models such as Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM) address this limitation through iterative latent-state refinement, they are typically task-specific and do not leverage pretrained language priors. We propose R-Qwen, a recursive reasoning framework built upon a pretrained Qwen backbone. R-Qwen repeatedly refines a candidate solution through programmatic self-recursion and deep supervision, combining the structured iterative computation of recursive models with the linguistic and reasoning priors of pretrained LLMs. We further adapt Hierarchical Supervision Weighting (HSW) to autoregressive models by exponentially weighting losses across recursive steps. HSW reduces gradient variance by at least 50\%, improves the signal-to-noise ratio of stochastic gradients, and accelerates convergence. Across eight challenging benchmarks, R-Qwen consistently outperforms prior recursive reasoning models and substantially larger LLMs while using a comparable number of trainable parameters. Notably, on ARC-AGI dataset, our model achieves a 27.6\% improvement over the baseline, highlighting the effectiveness of recursive refinement for general symbolic reasoning. These results suggest that recursive reasoning mechanisms and pretrained language model priors are complementary approaches for improving symbolic puzzle-solving. Code and models will be released after acceptance.

Function calling capabilities are crucial for deploying Large Language Models in real-world applications, yet current training approaches fail to develop robust reasoning strategies. Supervised fine-tuning produces models that rely on superficial pattern matching, while standard reinforcement learning methods struggle with the complex action space of structured function calls. We present a novel reinforcement learning framework designed to enhance group relative policy optimization through strategic entropy based exploration specifically tailored for function calling tasks. Our approach addresses three critical challenges in function calling: insufficient exploration during policy learning, lack of structured reasoning in chain-of-thought generation, and inadequate verification of parameter extraction. Our two-stage data preparation pipeline ensures high-quality training samples through iterative LLM evaluation and abstract syntax tree validation. Extensive experiments on the Berkeley Function Calling Leaderboard demonstrate that this framework achieves state-of-the-art performance among open-source models with 86.02\% overall accuracy, outperforming standard GRPO by up to 6\% on complex multi-function scenarios. Notably, our method shows particularly strong improvements on code-pretrained models, suggesting that structured language generation capabilities provide an advantageous starting point for reinforcement learning in function calling tasks. We will release all the code, models and dataset to benefit the community.

In recent years, various powerful policy gradient algorithms have been proposed in deep reinforcement learning. While all these algorithms build on the Policy Gradient Theorem, the specific design choices differ significantly across algorithms. We provide a holistic overview of on-policy policy gradient algorithms to facilitate the understanding of both their theoretical foundations and their practical implementations. In this overview, we include a detailed proof of the continuous version of the Policy Gradient Theorem, convergence results and a comprehensive discussion of practical algorithms. We compare the most prominent algorithms on continuous control environments and provide insights on the benefits of regularization. All code is available at https://github.com/Matt00n/PolicyGradientsJax.

We introduce ThinkTwice, a simple two-phase framework that jointly optimizes LLMs to solve reasoning problems and refine the answers, based on Group Relative Policy Optimization (GRPO). In each pair of training steps, ThinkTwice first optimizes the model on solving reasoning problems, then optimizes it on refining its own solutions to the same problems, using the same binary correctness reward in both phases without correctness signals or critique annotations. Across five mathematical reasoning benchmarks and two model families including Qwen3-4B and Olmo3-7B, ThinkTwice substantially improves both reasoning and refinement performance over competitive online policy optimization baselines. Specifically, on Qwen3-4B, ThinkTwice outperforms GRPO on AIME by 5 percentage points before refinement and by 11.5 points after one self-refinement step, measured by pass@4. Analysis of the training dynamics of ThinkTwice reveals an implicit rectify-then-fortify curriculum: refinement predominantly corrects errors early in training and naturally shifts toward preserving already-correct solutions as the model improves, yielding a more rectified reward signal. Our work establishes joint training of reasoning and self-refinement as a principled and effective methodology for RLVR.