Policy Learning

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79 papers in the last four weeks, up 316% on the four weeks before. 0.8% of all new papers.

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Latest papers 416

Jul 19, 2026cs.LG

Rethinking the Suitability of Reinforcement Learning Algorithms Under Practical Transfer Constraints

Transfer-oriented reinforcement learning requires evaluating algorithms along dimensions that go beyond standard sample efficiency. We focus on two dimensions: practical efficiency, which asks whether conclusions about algorithm suitability change under wall-clock rather than interaction-based budgets, and robustness under dynamics mismatch, which asks how different learning paradigms respond to variability in the training distribution induced by domain randomization. We provide two insights to reinforcement-learning practitioners. First, comparing the sample efficiency of different algorithms is often an insufficient criterion in transfer-oriented settings. The wall-clock time required to train a decent policy is an important consideration for practitioners, and we find that the sample-inefficient PPO algorithm can produce a performant policy faster than relatively more sample-efficient algorithms such as SAC and TD-MPC2, validating the common understanding of massively parallel training paradigms. Second, domain randomization can help different kinds of algorithms learn robust policies. In particular, although PPO, SAC, and TD-MPC2 represent different RL paradigms - on-policy, off-policy, and model-based learning and planning, respectively - we find that domain randomization affects all three algorithms in a similar way. To the best of our knowledge, this is the first controlled comparison of the effect of domain-randomization coverage on PPO, SAC, and TD-MPC2 under the same transfer protocol. Taken together, these two insights highlight the importance of evaluating RL algorithms not only by sample efficiency, but also by practical considerations such as training time and the algorithms' ability to produce usable policies.

Hany Hamed, Abhishek Naik, Colin Bellinger +1

University of Alberta · 3Alberta Machine Intelligence Institute (Amii) · 7Generative Bionics +4

Domain Randomization Reinforcement Learning Robust RL Policy Learning Sample-Efficient RL

Jul 17, 2026cs.AI

When to Plan: Learning to Select Between Reactive Control and Deliberative Planning

It has long been recognized that humans have the ability to switch between fast, reactive decision-making and slower, deliberative planning. In this paper, we study the question of how to learn this ability, known as meta-reasoning, in artificial agents. We model reactive decision-making as a policy that directly maps state observations to actions. Such policies can be trained with reinforcement learning (RL) or imitation learning, but may generalize poorly outside of their training distribution. Alternatively, model-based decision-time planning is more likely to produce good actions across a broader set of states but requires additional computation time, which delays acting. In this work, we introduce an RL method for training a meta-reasoning policy that allocates computation by conditioning on a reactive-policy uncertainty score. This score enables it to predict when the reactive policy is likely to perform poorly and when planning is needed. We conduct an empirical study on motion planning and navigation environments, showing that this design enables the meta-reasoning policy to learn when the reactive policy provides a good-enough action versus when decision-time planning is needed. Additionally, we show that our design enables the meta-agent to shift toward fully reactive control as the reactive policy improves.

Adam Labiosa, Josiah P. Hanna

Department of Computer Sciences, University of Wisconsin–Madison, USA

Robot Policy Learning Robotic RL Robotics Policy Learning

Jul 15, 2026cs.LG

Branching Policy Optimization: Sandbox-Native Language Agent Reinforcement Learning

Reinforcement learning has emerged as the dominant paradigm for training large language model (LLM) agents that interact with executable sandboxes. State-of-the-art algorithms such as PPO, RLOO, and GRPO inherit their rollout topology from RLHF: for each prompt, N independent trajectories are sampled from the initial state, and an advantage is computed by subtracting a group baseline. This design ignores a defining property of agent sandboxes. They are deterministic, snapshottable, and resumable from any intermediate state. We argue that this property enables a fundamentally different rollout topology: rather than N independent trees of depth T, one can construct a single tree of N leaves whose siblings share prefixes, and therefore share variance. We instantiate this idea as Branching Policy Optimization (BPO), a sandbox-native RL algorithm that (i) adaptively snapshots the sandbox at high-entropy decision points along a backbone trajectory, (ii) forks K alternative actions per branch point and rolls out each to termination, and (iii) computes per-step advantages from sibling returns rather than from independent prompts. We prove this estimator is unbiased and has strictly lower variance than the trajectory-level baseline, with the reduction equal to the prefix-explained portion of return variance. On WebShop, ALFWorld, and SWE-bench Verified with Qwen2.5-7B and Llama-3.1-8B backbones, BPO improves success by 3.6--6.1 absolute points over GRPO and RLOO at matched compute, halves gradient-norm variance, and matches the best baseline using 38% fewer policy updates.

Bowei He, Yankai Chen, Xiaokun Zhang +1

Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · McGill Univeristy, Montreal, Canada · City University of Hong Kong, Hong Kong SAR.

Reinforcement Learning Policy Gradient Methods Policy Learning Sample-Efficient RL RL for LLM Agents

Jul 14, 2026eess.SY

Environment Parameter Gradient Theorem for Policy-Environment Co-Design in Reinforcement Learning

Reinforcement learning (RL) is traditionally concerned with learning a control policy for a fixed environment. In many engineering systems, however, the environment itself is alterable: physical or operational parameters can be tuned to shape the transition dynamics and costs experienced by the agent. This motivates jointly optimizing both the policy and the environment design parameters. To this end, we establish an Environment Parameter Gradient Theorem -- a formal expression for the gradient of the value function with respect to environment parameters. The key theoretical device is a generalized action-value function

Q_{π,ξ}(s,a,ζ)

, which comprises two copies of the environment parameters:

ζ

governs the cost and transition dynamics at the current state--action pair, while

ξ

governs the future rollouts. This decoupling yields a tractable closed-form gradient expression and is essential to the theorem's derivation. Building on this result, we develop a model-free algorithm that simultaneously learns the optimal policy and the environment parameters. We demonstrate the efficacy of our framework on a UAV network design problem, where the optimal UAV placement (environment parameters) and communication routes (governed by the policy) are learned jointly to minimize the total communication cost in the network.

Amber Srivastava

Faculty of Mechanical Engineering, Indian Institute of Technology Delhi, India

Policy Learning

Jul 13, 2026cs.RO

Learning to Navigate with Minimal Parameters: Decomposing Visual Navigation Through Closed-Form Geometric Interfaces

Visual navigation policies have grown to hundreds of millions of parameters trained on billions of frames, with geometry, mapping, and control learned implicitly. We propose a decomposed point-goal navigation system in which operations with known closed-form structure, such as projective geometry, occupancy, and coordinate transforms, are computed analytically and serve as interfaces between three small learned modules: an egress predictor that grounds the episode goal as a local subgoal in the current view, a navigation predictor that estimates a goal-conditioned posterior over where trajectories travel, and an endpoint-pinned residual diffusion generator that samples trajectory shapes from this posterior. Only 0.58M out of 23M parameters are trained, on 44k frames, in under one GPU-hour. Across 6060 point-goal episodes in 60 environments, the system attains competitive success rates with the lowest collision rate among evaluated methods. We further show that under this decomposition, the frozen image encoder can be replaced by a 0.54M MobileNetV2 at a -2.0 SR cost, bringing the full system under 1.2M parameters. It also transfers to no-goal exploration by retraining only the 123k-parameter egress head, and its failure modes under sensor corruption are transparent and analytically correctable. We deploy and evaluate the system zero-shot on a low-cost UGV, running navigation and localization on a Jetson Orin Nano in real-time.

Edward Beng Wai Tan, Siew-Kei Lam

College of Computing and Data Science, Nanyang Technological University, Singapore.

Visual Navigation Robot Policy Learning Trajectory Generation Diffusion-Based Planning Robot Navigation Data-Efficient Robot Learning+1

Jul 13, 2026math.OC

Actor-Critic Learning for Extended Mean Field Control with Deterministic Policies

This paper develops a model-free reinforcement learning framework for continuous--time extended mean field control problems, where both the dynamics and reward may depend on the joint distribution of states and controls. We adopt deterministic feedback policies, under which the state--action distribution is induced directly as a push--forward of the state law. This avoids optimization over stochastic kernels and bypasses key limitations of existing approaches in extended mean field settings. We first establish a model--free sensitivity formula for parameterized McKean--Vlasov dynamics and use it to derive a deterministic policy gradient formula expressed through an advantage--rate function on the Wasserstein space. We then refine this formula by introducing local value and advantage--rate representations that depend on the state, action, and joint state--action distribution, yielding a policy gradient that includes both action derivatives and measure--derivative terms with respect to the control distribution. These characterizations lead to a martingale--based learning principle and motivate a continuous--time deep deterministic policy gradient algorithm combining particle approximations, measure--dependent neural networks, temporal--difference learning, and exploration in either action or parameter space. Numerical experiments on stochastic Cucker--Smale consensus control and optimal liquidation with trade crowding demonstrate the efficiency, stability, and robustness of the proposed method, including problems with explicit dependence on the control distribution.

Ziheng Cheng, Xin Guo, Huyên Pham +1

University of California, Berkeley · Ecole Polytechnique, CMAP · Imperial College London

Policy Gradient Continuous-Time RL Model-Free RL Deep Deterministic Policy Gradient Actor-Critic Methods Policy Learning

Jul 9, 2026cs.LG

SafeExplorer: An Unbiased Policy Gradient for Reinforcement Learning with Recovery Interventions

Training reinforcement-learning agents directly on physical robots makes every fall costly, since a fall can damage the platform and cannot be undone like a simulator reset; the goal is therefore to minimize falls during training rather than trade them off against return, as constrained Markov decision process (MDP) formulations do. A standard mitigation hands control to a separate recovery policy whenever the agent leaves a designer-specified safe region (a subset of state space it should stay within), but the resulting mixed-policy rollouts silently bias every on-policy update, and the importance-sampling correction that would remove this bias is ill-defined whenever the recovery policy is deterministic. We address this bias with a drop-in modification of proximal policy optimization (PPO). Its core is an unbiased policy-gradient estimator that uses the score function only at safe timesteps and never evaluates the recovery policy's density, so it stays valid even when the recovery policy is deterministic, exactly where importance sampling breaks, and it empirically dominates importance sampling even when the recovery policy is stochastic. Because the recovery policy still makes credit assignment slow near the safe-region boundary, two further components accelerate learning: a closed-form value for recovery-triggering states when dynamics and recovery are deterministic, and an imitation loss that copies recovery actions only when recovery succeeds. On a three-environment, five-seed benchmark, the resulting algorithm reduces training-time falls by factors of 233x, 48x, and 26x on HalfCheetah, Ant, and Unitree Go1 over standard PPO, while matching or exceeding PPO's final reward, and on Ant, where the recovery policy is unreliable, it is the only method that reaches 80% of the best final reward.

Elham Daneshmand, Majid Khadiv, Glen Berseth +1

McGill University · Mila · Technical University of Munich +1

Robot Safety Proximal Policy Optimization Safe RL Policy Learning

Jul 9, 2026cs.LG

Prompt-Driven Exploration

Exploration is essential to RL since a policy cannot improve by repeatedly sampling the behaviors it already prefers. Standard methods inject stochasticity in the action space, but such jitter only yields rollouts close to the original. Escaping a weak policy often requires global perturbations that action noise cannot produce. Large language models (LLMs) and vision-language-action (VLA) models offer a pathway: they condition the policy on a natural language prompt, and since the rollout follows from it, modifying the prompt induces global changes. The challenge is finding prompts that induce useful global changes. With a weak policy that rarely succeeds, reward is too sparse to select on. Our idea is to refine prompts from the rollouts themselves: a vision-language model (VLM) reasons over the rollout video, diagnoses how the policy responded, and rewrites the prompt to elicit better behavior next time. This procedure resembles posterior sampling, a classical RL exploration framework, at the level of prompts: the VLM maintains an implicit distribution over useful prompts and updates it from observed rollouts. We call this strategy Prompt-Driven Exploration (PDE). Across manipulation and reasoning tasks, PDE enables RL to learn successful policies even from zero-reward starts, and improves sample efficiency more broadly. Our website is available at https://xinyunsunshine.github.io/prompt-rl.

Sunshine Jiang, John Marangola, David Zhang +6

Massachusetts Institute of Technology · Improbable AI Lab · MIT-IBM Computing Research Lab

LLM-Guided RL RL Exploration Policy Learning Sample-Efficient RL

Jul 9, 2026cs.LG

Latent Memory Palace: Reasoning for Control as Autoregressive Variational Inference

Human decision-making is highly flexible -- some actions are taken immediately; others require longer deliberation. Language models have exhibited a similar capacity for adaptive "reasoning." However, transferring this capability to continuous control policies has been challenging, as directly reasoning in language space may lack the granularity for spatial understanding and precise motions. In this work, we show that reasoning for control policies can emerge by organizing information in an autoregressive latent space reminiscent of a memory palace, where retrieval is iterative and adaptive. Our method, Latent Memory Palace (LMP), formulates reasoning as variational inference with an autoregressive latent distribution. We derive a latent-space reinforcement learning technique to tractably optimize its variational lower bound. The resulting policy, LMP-

π

, achieves strong empirical performance in simulation and real-world domains while exhibiting interpretable, adaptive allocation of test-time compute. We further show that the same framework yields a variable-length action tokenizer, LMP-

\texttt{tok}

, which significantly improves the performance of downstream autoregressive policies. Together, these results present a new perspective on latent reasoning for control through the lens of variational inference.

Chuning Zhu, Eva Xu, Jose Barreiros +3

University of Washington · Toyota Research Institute

RL Control Latent Action Learning Variational Inference Policy Learning

Jul 8, 2026stat.ML

Expressivity and Statistical Trade-offs in Diffusion Policy Learning

Diffusion-based policies have recently emerged as powerful policy parameterizations for reinforcement learning, representing state-conditioned action distributions as terminal laws of diffusion processes with parameterized drifts. This terminal-law representation has shown substantial expressive flexibility in practice, enabling diffusion policies to model complex, multimodal, and highly non-Gaussian action distributions; however, it remains unclear what mathematically drives this expressivity and how to fully exploit it when the policy is learned from finite data. In this paper, we identify the drift Lipschitz budget

K

as a central quantity governing the expressivity and statistical behavior of diffusion policies. We quantify expressivity through approximation: diffusion policies with

K

-Lipschitz drifts can concentrate near optimal deterministic policies and achieve value approximation error of order

1/K

; moreover, we prove a matching lower bound under nondegenerate diffusion noise. This increased expressivity comes with a statistical cost. When the drift is parameterized by neural networks, increasing

K

improves approximation but increases statistical complexity. Balancing these two terms yields a finite-sample performance gap of order

\tilde{O}(n^{-2/(m+6)})

for generic neural-network drifts, and a sharper rate

\tilde{O}(n^{-2/(m+4)})

for one-sided dissipative drift classes, where

n

is the sample size and

m

is the dimension of the state space. Numerical experiments provide empirical evidence for the sample-dependent trade-off in

K

, supporting both theoretical regimes. Our framework also suggests a practical implementation principle: choose the diffusion budget

K

according to the available sample size, and then select a neural-network architecture with the corresponding fixed Lipschitz coefficient.

Viet Vu, Renyuan Xu, Jiacheng Zhang +1

Stanford University · Chinese University of Hong Kong · Imperial College London

Diffusion Policy RL for Diffusion Models Policy Learning

Jul 8, 2026cs.LG

NFTR: From Provable Mode-Averaging to Geodesic Subgoal Selection in Offline Goal-Conditioned RL

Hierarchical Implicit Q-Learning (HIQL), an offline goal-conditioned RL method, selects subgoals by value-function advantages alone. This rule has two coupled failure modes. Optimistic bias treats lucky stochastic outcomes as skillful choices, and mode collapse reduces a multi-modal subgoal distribution to a single Gaussian mean that often falls in unreachable regions. We propose NFTR (Normalizing Flow subgoal policies with Triangle-slack Reweighting). A conditional Normalizing Flow replaces the Gaussian policy. A closed-form mode-averaging result identifies the Gaussian limitation, while conditional flows support multi-modal weighted maximum likelihood and direct sampling. A triangle slack score, computed from a jointly trained MRN distance head whose triangle inequality is guaranteed architecturally, corrects the AWR weight multiplicatively and measures a detour inside the learned geometry without requiring exact distance recovery. Triangle-slack vanishes on geodesics in deterministic MDPs and remains a conservative upper bound on composability violation under stochastic dynamics. The RWDR objective preserves AWR's population-level monotonic improvement and admits a three-term suboptimality decomposition. On OGBench the flow carries the larger share of the gain, while the full co-trained configuration adds task-dependent gains. The combined method avoids Gaussian mode averaging and performs well on stochastic tasks. GitHub page: https://github.com/erdemtbao/NFTR

Erdemt Bao, Xing Lei, Jun Chen +2

Huazhong University of Science and Technology · Xi’an Jiaotong University · University of Electronic Science and Technology of China

Normalizing Flows Hierarchical RL Offline RL Policy Learning

Jul 7, 2026cs.RO

Optimal Transport Q-Learning for Flow Policy Steering and Acceleration

Diffusion and flow policies have recently demonstrated remarkable performance in robotic applications by accurately capturing multimodal robot trajectory distributions, especially in the context of vision language action (VLA) models. However, high quality policy performance also requires fast inference and high quality demonstrations, which are often hard to get. Lack of these leads to suboptimal policy behaviors and failure under distribution shifts. In this work we address the problem of fine-tuning and accelerating suboptimal flow-based policies using the robot's experience through RL post-training. We introduce Optimal Transport Q-Learning (OTQL), a new method for finetuning flow policies using advantage weighted conditional optimal transport flow matching. OTQL can finetune and accelerate flows with an interaction budget of 50-60 episodes while avoiding computationally expensive distillation in simulation and real-world robot tasks. Our results show that OTQL post-trains flow policies using the robot's own experience, increasing average success percentage of single-task policies from 36% to 86% and of a pre-trained VLA from 38% to 76% while reducing the number of inference steps per action generation by 70%.

Andreas Sochopoulos, Esmeralda S. Whitammer, Nikolaos Tsagkas +3

University of Edinburgh · 2Honda Research Institute Europe

Robot Policy Adaptation Q-Learning Robotic RL RL Post-Training VLMs for Robotics Policy Learning

Jul 6, 2026cs.LG

Weak-to-Strong Generalization via Direct On-Policy Distillation

Reinforcement learning with verifiable rewards (RLVR) is a powerful recipe for improving language-model reasoning, but it is expensive to repeat on every new strong model because the target model must generate many rollouts during training. As models scale, post-training itself becomes a bottleneck. We study a weak-to-strong alternative: run RL on a smaller model where rollouts are cheaper, then reuse what that RL run learned to improve a stronger target model. Directly distilling the post-RL weak teacher is not enough, because the teacher's final policy mixes useful RL gains with the limitations of the smaller model. We propose Direct On-Policy Distillation (Direct-OPD), which transfers the teacher's RL-induced policy shift instead. Direct-OPD compares the post-RL teacher with its own pre-RL reference and treats their log-ratio as a dense implicit reward for the student. In plain terms, the checkpoint pair tells us which actions RL made the weak model more or less likely to take, and Direct-OPD applies that signal on the stronger student's own on-policy states. This directly reuses the weak model's RL supervision signal without running sparse-reward RL on the target model. Empirically, Direct-OPD consistently leverages weaker teachers to improve stronger target models; notably, it boosts Qwen3-1.7B from 48.3% to 58.3% on AIME 2024 in just 4 hours on 8 A100 GPUs. It outperforms step-matched direct RL and enables the sequential composition of multiple policy shifts. Our results show that RL outcomes can be reused across model scales as implicit reward signals, not merely as final models to imitate.

Shiyuan Feng, Huan-ang Gao, Haohan Chi +7

1SIA-Lab of Tsinghua AIR and ByteDance Seed · Institute for AI Industry Research (AIR), Tsinghua University · 4Peking University +1

RL for Language Model Reasoning Weak-to-Strong Generalization Reinforcement Learning with Verifiable Rewards On-Policy Distillation Policy Learning

Jul 6, 2026cs.LG

TREK: Distill to Explore, Reinforce to Refine

Group Relative Policy Optimization (GRPO) is effective when the current policy already samples useful reasoning trajectories, but it stalls on hard prompts whose correct solution modes lie outside the student's on-policy support. We propose TREK (Teacher-Routed Exploration via Forward KL), a simple staged procedure that uses distillation not for imitation but for exploration support expansion. A key advantage of TREK is its generality: because it only consumes verified output trajectories, it can use an external black-box teacher, a white-box teacher, or the same model given additional inference-time context, and it can efficiently identify which hard-prompt samples are most worth consolidating even when teacher internals are unavailable. TREK first identifies prompts where the unaided student has very low pass rate, queries a proposal source to produce verified candidate solutions, keeps the top-

r

proposals ranked by current student likelihood, applies a short forward-KL phase to pull those verified modes into the student's support, and then returns to standard on-policy GRPO refinement. On mathematical reasoning, TREK with DeepSeek-V4 proposals improves Qwen3 models across all tested scales on AIME 2024 and AIME 2025; for Qwen3-8B, it improves AIME 2025 from 36.9 to 40.3 and AIME 2024 from 47.9 to 51.1 (avg@16), while the self-context variant reaches 38.5 and 49.6 without an external teacher. On agentic tasks, TREK raises ALFWorld success rate from 75.8 to 82.8 and ScienceWorld success rate from 12.5 to 26.7; notably, on the hardest task types, TREK achieves high success rates early in training while unaided GRPO requires substantially more optimization steps to reach comparable levels.

Yuanda Xu, Zhengze Zhou, Kayhan Behdin +10

LinkedIn Corporation · Harvard University · Georgia Institute of Technology

RL for Language Model Reasoning LLM-Guided RL RL Exploration Policy Learning RL for LLM Agents

Jul 6, 2026cs.LG

Multi-Turn On-Policy Distillation with Prefix Replay

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 4

\times

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.

Baohao Liao, Hanze Dong, Christof Monz +3

1Microsoft Research · University of Amsterdam

LLM Agent Training On-Policy Distillation Policy Learning RL for LLM Agents

Jul 6, 2026cs.LG

Trust Region Policy Distillation

Big goals are hard to achieve all at once; breaking them into small steps is wiser. We present Trust Region Policy Distillation (TOP-D), which transforms the notoriously unstable, high-variance On-Policy Distillation (OPD) into a stable training paradigm by dynamically constructing a proximal teacher. Theoretically, we establish a rigorous framework demonstrating that TOP-D inherently controls gradient variance. By providing a formal global convergence analysis alongside a monotonic improvement bound, we mathematically formalize the reliability and stability of the overall training dynamics. Empirically, TOP-D dramatically enhances training stability, sample efficiency, and final performance on mathematical reasoning tasks. More importantly, TOP-D introduces zero additional computational overhead, positioning itself as a promising alternative to the well-established OPD paradigm.

Zhengpeng Xie, Li Lyna Zhang, Zeke Xie +1

On-Policy Distillation Policy Learning Policy Distillation Knowledge Distillation

Jul 3, 2026stat.ML

A Hierarchy of Policy Learning Problems

Policy learning has received substantial attention with the goal of learning policies from observational data for decision-making. A majority of work in this space has focused on developing algorithms for computing policies that minimize regret compared to the optimal policy. However, in many practical settings, there is insufficient data to obtain low regret. As a result, recent work has shifted attention to alternative objectives, most notably, studying whether it is possible to learn an improving policy that statistically significantly outperforms baseline policies. We argue that there is substantial merit in studying a broader range of policy learning problems. When there is insufficient data to learn an improving policy, there may still be useful questions that can be answered. To this end, we provide a mathematical framework for studying the relationships between policy learning problems. We formalize three problems within our framework: beyond the optimal policy problem and the improving policy problem, we also propose the policy existence problem, which aims to determine if an improving policy exists. Within our framework, we show that the policy existence problem reduces to the improving policy problem, which in turn reduces to the optimal policy problem; these reductions prove that each problem is at least as easy as the next one (in sample complexity). A key question remains: is this hardness strict? We provide partial answers. First, the gap between the optimal policy and improving policy problems is strict. For the improving policy and policy existence problems, we prove that a sublinear polynomial gap exists under natural conditions on improving policy learning algorithms. Thus, we may be able to answer questions about the existence of an improving policy even when we cannot find one. These results highlight the value in studying a broader range of policy learning problems.

Hamsa Bastani, Osbert Bastani, Shihan Chen

Wharton School, University of Pennsylvania · University of Pennsylvania · Graduate Group in Applied Mathematics and Computational Science, University of Pennsylvania

Sample Complexity Offline RL Policy Learning

Jul 3, 2026cs.LG

ACPO: Adaptive Credit Policy Optimization via Fine-Grained Surrogate Entropy

Reinforcement Learning (RL) has substantially improved the reasoning ability of large language models (LLMs), but sparse outcome rewards still make token-level credit assignment difficult. Existing scalable RL methods typically assign trajectory-level rewards uniformly across tokens, while recent entropy-aware approaches either rely on coarse detached heuristics or directly optimize true entropy, which can introduce non-local gradient components misaligned with sampled-token policy updates. We propose Adaptive Credit Policy Optimization (ACPO), a token-level credit assignment framework based on a mode-local surrogate entropy. ACPO asymmetrically modulates policy updates by emphasizing uncertain decisions in successful rollouts and overconfident tokens in failed rollouts. We show that the surrogate admits deterministic entropy bounds and, under modal alignment and proximal updates, preserves the policy-gradient direction to leading order. Experiments on mathematical reasoning and coding benchmarks, including AIME 2025 and HumanEvalPro, show that ACPO consistently improves over strong RL baselines such as DAPO, GTPO, and SAPO.

Zijun Xie, Yuyang You, Yongzhi Li +6

Peking University · Baidu Inc. · Kuaishou Inc.

Token-Level Credit Assignment RL for Language Model Reasoning Step-Level Credit Assignment in RL Maximum Entropy RL Policy Gradient Methods Sparse-Reward RL+1

Jul 2, 2026cs.AI

ASK in the Dark: Uncertainty-Gated LLM Assistance under Partial Observability

Reinforcement learning agents operating under partial observability must act on incomplete information, making them natural candidates for guidance from small language models (SLMs) that carry broad reasoning priors. Yet integrating SLM guidance into this setting has proven difficult: across all test environments, vanilla uncertainty-gated approaches achieve an overwrite rate at or near zero, meaning the SLM almost never contributes an independent action. We trace this failure to the bare egocentric prompt, which provides insufficient context for genuine reasoning, and identify it as a context problem rather than a capacity problem. We propose ASK+, which supplies the SLM with trajectory-aware context (a partially revealed map, visited positions, and action history) and structured chain-of-thought reasoning, converting it from a passive redundancy check into a more informative consultant that occasionally corrects the policy. We further establish that the predictive entropy signal used for selective querying measures action uncertainty rather than state uncertainty and remains informative in POMDPs, making uncertainty-gated assistance viable beyond fully observable settings. The stateful prompt drives substantial gains: on DoorKey, where vanilla ASK matches PPO (both 89%), ASK+ reaches 93% success; on FourRooms, success climbs from 53% to 70%; on HigherLower, accuracy reaches 73.7%, matching the SLM-only upper bound. Across all environments, Qwen3.5-2B matches or exceeds Qwen3.5-4B, confirming that prompt design and selective gating dominate the impact of model scale, enabling guidance without large models.

Juarez Monteiro, Nathan Gavenski, Guilherme Lima +3

Kunumi Institute, Belo Horizonte, MG, Brazil · King’s College London, London, United Kingdom

Partially Observable RL LLM Prompting LLM-Guided RL Policy Learning

Jul 2, 2026cs.RO

Learning Agile Intruder Interception using Differentiable Quadrotor Dynamics

This paper presents a methodology for learning a control policy to intercept an intruder using the 3D direction unit vector to the intruder and the interceptor state. Prior deep reinforcement learning approaches assume either relative position or distance to the intruder is available, but this information is not readily accessible in real-world applications that employ passive, monocular camera sensors. Instead, we propose a solution that leverages an analytical policy gradient method using differentiable quadrotor dynamics to learn agile interception at speeds up to 10 m/s. The proposed approach outperforms baseline methods that utilize simplified point mass dynamics by an average of 30%.

Michael Anoruo, Xiaoyu Tian, Abhishek Rathod +5

Carnegie Mellon University · Artificial Intelligence Integration Center

RL Control Robot Policy Learning Quadrotor Control Policy Learning

Jul 1, 2026math.OC

Mean Field Reinforcement Learning

This monograph provides an introduction to mean field reinforcement learning through the lens of Markov decision processes arising from large-population stochastic control with mean field interactions and common noise. Starting from the connection between multi-agent reinforcement learning and mean field control, it develops the probabilistic, mathematical, and control-theoretic framework needed to formulate representative-agent learning problems, analyze their relationship with finite-population systems, and study both general and linear-quadratic models. The presentation includes dynamic programming principles, propagation-of-chaos limits, and theoretical analyses of tabular Q-learning and policy-gradient methods. It also discusses numerical implementations, including tabular schemes and deep reinforcement learning methods such as deep deterministic policy gradient. The goal is to give readers a coherent bridge between mean field control theory and reinforcement learning methodology, emphasizing the mathematical structure of the problems and the design of tractable learning approaches for large stochastic populations.

René Carmona, Mathieu Laurière

Department of Operations Research and Financial Engineering & Program in Applied and Computational Mathematics, Princeton NJ 08544, USA · Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning; NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai; NYU Shanghai, 567 West Yangsi Road, Shanghai, 200126, People’s Republic of China

Reinforcement Learning Q-Learning Policy Gradient Methods Policy Learning

Jul 1, 2026cs.LG

Don't Let Gains FADE: Breaking Down Policy Gradient Weights in RL

Reinforcement learning post-training dramatically improves LLM reasoning, but suffers from training instability and diversity collapse. Advantage functions offer an appealing fix: they reshape the training objective, reweight which rollouts drive learning, and are trivial to implement. Yet a proliferation of methods makes it unclear which advantage to use and when. We cut through the confusion with a unifying framework that decomposes any advantage into its positive and negative gradient mass along two orthogonal axes. On the sign axis, imbalanced updates collapse either entropy or weight geometry. On the difficulty axis, hard-problem focus sharpens signal but costs sample size. Both trade-offs shift during training: exploration favors balance and hard focus; exploitation favors suppression and medium focus. This motivates FADE (Focal Advantage with Dynamic Entropy), a self-adapting advantage that reads training dynamics to schedule the gradient weight automatically. FADE reaches peak pass@1 20k steps earlier than the best static baseline at the 7B scale and 2k steps earlier at the 32B , while achieving the best accuracy-diversity trade-off across all pass@k on LiveCodeBench and AIME.

Juliette Decugis, Sean O'Brien, Francis Bach +2

FAIR at Meta · Work done at Meta, now working at the University of California, San Diego · Inria, Ecole Normale Supérieure

Policy Gradient RL for Language Model Reasoning RL Post-Training Policy Learning

Jul 1, 2026cs.AI

Procedural Memory Distillation: Online Reflection for Self-Improving Language Models

Reinforcement learning with verifiable rewards (RLVR), along with recent selfdistillation variants such as SDPO, evaluates each rollout against a verifier and updates the policy from that episode-level signal. However, the richer procedural information in the rollout is rarely retained or reused. Across episodes and epochs, the model repeatedly encounters related problems under a changing policy, producing cross-episode signals that episode-local updates cannot capture: which strategies consistently pass verification, which failure modes persist, which patterns recur. We propose Procedural Memory Distillation (PMD), which converts these crossepisode signals into reusable procedural memory and distills it into the policy's weights during training. This memory functions as a training scaffold, absorbed into the policy itself, yielding a memory-free model at inference. PMD organizes the memory at three levels of abstraction: raw trajectories, self-reflected strategies and lessons, and higher-level behavioral patterns that recur across problems, all extracted online from the model's own trajectories. A memory-conditioned self-teacher draws on the accumulated experience to supervise the student on its own rollouts, enabling student to progressively internalize procedural knowledge within its parameters. The central design principle is co-evolution: the policy generates rollouts that update the memory, and memory shapes the supervision that updates the policy. Empirically, across Qwen3-8B and OLMo3-Instruct-7B, PMD improves over SDPO by 3.8-5.5% on SCIKNOWEVAL and 7.9-13.6% on LIVECODEBENCH. Co-evolution powers these gains: freezing either the memory or the policy trails PMD by more than 10% across SCIKNOWEVAL domains.

Ye Liu, Srijan Bansal, Bo Pang +6

Salesforce AI Research

Language Model Distillation Reinforcement Learning with Verifiable Rewards RL Post-Training Policy Learning

Jul 1, 2026cs.RO

Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications

Reinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that limit both interpretability of learned policies and lack explicit control over gait behaviors. We introduce a framework where distinct gaits are specified using parameterized constraints expressed in Signal Temporal Logic (STL). These include safety bounds, gait synchronization constraints, command tracking, and actuation bounds. From these specifications, we develop a reward shaping mechanism that provides learning agents a dense, continuous reward landscape that encodes desired behavior. We define parametric STL templates for three speed regimes (walking-trot, trot, bound), calibrate their parameters from reference rollouts, and compute rewards from using smooth approximations of STL robustness over the rollouts. The generated rewards can be used to provide shaped gradients compatible with Proximal Policy Optimization (PPO). We instantiate the approach on Google's Barkour quadruped robot in MuJoCo XLA (MJX). We use parallelization within the simulator to improve training speeds and use domain randomization to robustify learned policies. We show that compared to a baseline of hand-crafted rewards, the STL-shaped rewards yield tighter velocity tracking and more stable training. Videos can be found on our project website: https://stl-locomotion.github.io/.

Merve Atasever, Cagan Bakirci, Alfredo Reina Corona +2

University of Southern California, Los Angeles, California, USA

Reinforcement Learning Robot Skill Learning RL for Legged Locomotion Policy Learning Reward Design for RL Quadruped Locomotion

Jun 30, 2026cs.RO

Freeform Preference Learning for Robotic Manipulation

Reward design remains a central bottleneck for autonomous robot policy improvement, especially in long-horizon manipulation tasks where sparse success labels provide too little signal and binary preferences collapse many competing notions of quality into one ambiguous signal. We introduce Freeform Preference Learning (FPL), a method for learning robot policies from freeform human preferences. Rather than asking annotators which of two trajectories is better overall, FPL lets them define natural-language preference axes, such as speed, safety, quality of placement, or carefulness, and provide pairwise preferences along each axis. These annotations are used to learn a language-conditioned reward model that maps a trajectory and preference label to an axis-specific reward. We use this model to train a reward-conditioned policy that optimizes across the multiple human-specified dimensions. Across four real-world and two simulated long-horizon manipulation tasks, FPL improves over sparse-reward and binary-preference methods by 38 percentage points. Beyond improved performance, FPL learns dense progress signals without explicit subtask segmentation, shows compositionality of behavior not present in the data, and allows users to steer the policy towards different behaviors at test time without retraining. Blog post with videos available at https://freeform-pl.github.io/fpl.website/

Marcel Torne, Anubha Mahajan, Abhijnya Bhat +1

Stanford University

Long-Horizon Robotic Manipulation Robot Skill Learning Robotic Manipulation Policy Learning Preference-Based RL

Jun 30, 2026cs.LG

TRIAGE: Role-Typed Credit Assignment for Agentic Reinforcement Learning

Agentic reinforcement learning requires assigning credit to environment-facing actions such as searches, clicks, edits, navigation commands, and object interactions. Standard GRPO uses the final verifier outcome as a uniform advantage over all action tokens. This outcome signal is useful but structurally incomplete: it punishes useful exploration in failed rollouts and reinforces redundant or regressive actions in successful rollouts. We propose TRIAGE, a role-typed credit assignment framework that adds a semantic role axis to outcome credit. A structured judge classifies each segment as decisive progress, useful exploration, no-progress infrastructure, or regression, and a fixed role-conditioned rule maps these labels to bounded segment-level process rewards. This keeps verifier outcomes as the source of optimization direction while correcting the two main blind spots of outcome-only credit. We further show that role-conditioned credit is the optimal segment-level correction expressible from role labels alone -- a projection of the per-segment advantage residual onto the role variable -- so that the fixed role constants reduce advantage estimation error whenever the judge is reliable, and we connect this to lower-variance policy gradients. Across ALFWorld, Search-QA, and WebShop, TRIAGE improves success rates over GRPO for two policy models and outperforms both a scalar judge-derived process reward and an outcome-supervised shared-backbone value baseline. Ablations show that the gain comes from role typing rather than merely adding dense rewards: reliable detection of regression inside successful trajectories is the dominant contributor, while exploration credit provides a consistent secondary gain; on completed ALFWorld and WebShop rollouts, TRIAGE also reduces environment-facing turns by an additional

10.4\%

and

14.8\%

relative to GRPO.

Yuanda Xu, Zhengze Zhou, Hejian Sang +6

1LinkedIn Corporation · 2Harvard University · 3Johns Hopkins University +1

Agentic RL Step-Level Credit Assignment in RL Credit Assignment Policy Learning Reward Design for RL Fine-Grained Credit Assignment+1

Jun 29, 2026cs.AI

HyPOLE: Hyperproperty-Guided Multi-Agent Reinforcement Learning under Partial Observation

Formal specification is a powerful tool to guide the learning process and provides significant advantages over reward shaping: (1) mathematical rigor; (2) expressiveness to specify objectives and constraints, and (3) the ability to define tactics to achieve objectives. However, these benefits remain largely unexplored in the context of Multi-Agent Reinforcement Learning (MARL). This paper introduces HyPOLE, a novel framework for MARL under partial observability, where learning is guided by the expressive power of the so-called hyperproperties and, in particular, the temporal logic HyperLTL. We integrate Centralized Training for Decentralized Execution (CTDE) techniques with HyPOLE to synthesize decentralized policies, and our evaluation on SMAC, MessySMAC, and WildFire benchmark demonstrates clear advantages over baselines.

Arshia Rafieioskouei, Tzu-Han Hsu, Matthew Lucas +1

Department of Computer Science and Engineering, Michigan State University, MI, USA.

Reinforcement Learning Partially Observable RL Decentralized MARL Policy Learning Multi-Agent Reinforcement Learning

Jun 29, 2026cs.LG

Predictable GRPO: A Closed-Form Model of Training Dynamics

We develop a first-principles reduced-order model of these dynamics. Under a single mean-field assumption that summarizes the policy by its expected reward, we reduce the GRPO update to a stochastically-forced damped oscillator whose mass, damping, and stiffness are fixed in closed form by the optimizer hyperparameters together with a single measured curvature scale -- momentum supplies the inertia, off-policy lag erodes the damping, and the group size enters, to leading order, as a noise temperature. The reduction has three consequences. First, it subsumes the empirical single-exponential saturation law as its overdamped limit, recasting the fitted plateau, timescale, and size exponent as the fixed point, inverse stiffness, and curvature-scaling exponent of the underlying potential, and adding, through the retained inertial term, the slow-start phase the single exponential cannot represent. Second, it yields predictions tied to independently measurable quantities rather than fitted ones: group-size invariance of the deterministic trajectory with a

1/G

stationary fluctuation, a sharp stability threshold in the refresh interval, and an overdamped-to-oscillatory transition. Third, it furnishes diagnostics that separate failure modes a reward curve alone conflates -- reward hacking, advantage degeneracy, policy concentration, and dynamical instability. Across three models and two group sizes, the closed-form trajectory fits training reward to

R^2 \geq 0.91

and the mean trajectory is group-size invariant to leading order -- on both the reward curve and out-of-distribution transfer to eight math benchmarks -- while the within-group reward spread retains a residual

G

-dependence that the leading-order temperature picture does not capture.

Rajat Ghosh, Datta Nimmaturi, Aryan Singhal +4

Nutanix San Jose, USA · Unsloth Hyderabad, India · Nutanix2026 San Jose, USA +1

Group Relative Policy Optimization Policy Optimization Neural Network Training Dynamics Policy Learning Gradient Descent Dynamics

Jun 29, 2026cs.LG

Pessimism's Paradox: Conservative Offline Training Amplifies Reward Hacking During Online Adaptation in Reasoning Models

Conservative offline training is widely advocated as a safe foundation for subsequent online adaptation: if a policy stays close to well-supported behaviour, the argument goes, it is less likely to exploit imperfections in a learned reward model. We challenge this intuition empirically and mechanistically. We train a Qwen3-14B policy under Direct Preference Optimisation (DPO) with three levels of conservatism (

β\in \{β_{\mathrm{lo}}, β_{\mathrm{mid}}, β_{\mathrm{hi}}\}

derived from empirical log-ratio percentiles), then adapt each checkpoint online against a learned reward ensemble (3,

\times

,Qwen3-1.7B) while measuring true performance on GSM8K exact-answer accuracy. We find that \emph{higher offline conservatism monotonically increases reward-hacking damage}, measured by the Goodhart gap and its area under the curve (AUGC), with Spearman

ρ= 1.0

across all three conditions. Mechanistic analysis reveals a three-link causal chain: (i) high-

β

DPO compresses policy entropy, (ii) Low-entropy policies generate responses with reduced diversity, concentrating in a narrow region of the reward model's training distribution (lower pairwise cosine distance), and (iii) despite this proximity, ensemble disagreement (epistemic uncertainty) increases with

β

and is exploited faster during online optimisation. We further fit a power-law curve to the

(β, \augc)

data and identify a practical optimal conservatism level

β^{\star}

that balances alignment fidelity against hacking vulnerability. Our results suggest that the field needs \emph{calibrated}, not \emph{maximal}, conservatism.

Subramanyam Sahoo, Aman Chadha, Vinija Jain +1

1Horizon Research · 2Apple · 3Meta +1

Reward Modeling Reward Hacking RL for Language Model Reasoning Offline RL Policy Learning Offline-To-Online RL

Jun 29, 2026cs.AI

ACPO: Agent-Chained Policy Optimization for Multi-Agent Reinforcement Learning

Cooperative tasks in Multi-Agent Reinforcement Learning (MARL) require agents to collectively maximize a shared return. Under the Centralized Training with Decentralized Execution (CTDE) paradigm, policy gradients have remained difficult to compute directly. Prior methods largely follow two approaches: independent factorized updates with centralized critics, which lack general joint-improvement guarantees without value decomposition assumptions, or alternating best-response updates, which can converge to suboptimal Nash Equilibria. In this paper, we show the joint policy gradient admits an exact decentralized decomposition of per-agent terms, each formed from per-agent score functions and decentralized critics. Based on this decomposition, we develop Agent-Chained Policy Optimization (ACPO), where actors are trained independently, with their updates together constituting a single step on the joint policy gradient. Central to this result is a serialized view of the simultaneous joint decision in which agents commit actions one at a time, each conditioning on a belief over preceding actions. The belief acts as the coordination mechanism which ties the independent per-agent updates into a joint gradient step. We evaluate ACPO on Multi-Robot Warehouse, SMACv2, and MA-MuJoCo, where it outperforms strong baselines, with the gap widening as the number of agents grows.

Daiki E. Matsunaga, Junho Na, Tri Wahyu Guntara +4

1KAIST · 2KRAFTON · University of Toronto +2

Multi-Agent System Optimization Multi-Agent Coordination Decentralized MARL Policy Learning Cooperative MARL Multi-Agent Reinforcement Learning