Policy Gradient Methods

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7 papers in the last four weeks, up 133% on the four weeks before. 0.1% of all new papers.

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Latest papers 108

Jun 22, 2026cs.LG

EMAgnet: Parameter-Space EMA Regularization for Policy Gradient Self-Play in Large Games

Recent work has established that regularized policy gradient methods such as PPO, when used in self-play, can match or exceed specialized game-theoretic algorithms for solving two-player zero-sum imperfect-information games. The uniform distribution has emerged as a strong policy regularization target for this purpose, but it regularizes equally toward all actions regardless of their viability. We introduce EMAgnet, which instead regularizes toward an exponential moving average (EMA) of the last-iterate policy's parameters, providing an adaptive regularization target that evolves with the agent's improving strategy. We evaluate EMAgnet on both standard two-player zero-sum benchmarks and modified benchmarks with exploration challenges and large numbers of strictly dominated strategies. Relative to PPO self-play with uniform-magnet regularization under both linear and power-law annealing schedules, EMAgnet achieves lower exploitability in the majority of tested environments, with consistent performance gains across games containing strictly dominated strategies.

Tristan Maidment, JB Lanier, Chase McDonald +5

1Riot Games · 3New York University · University of California, Irvine

Self-Play RL Imperfect-Information Games Zero-Sum Games Policy Gradient Methods Proximal Policy Optimization Policy Learning

Jun 22, 2026cs.LG

KLip-PPO: A per-sample KL perspective on PPO-Clip

Proximal Policy Optimization (PPO) is the standard policy-gradient algorithm for on-policy reinforcement learning. The literature presents it in two forms, a clipped surrogate that bounds the importance ratio between successive policies and a Kullback-Leibler penalty between them. These forms are treated as separate algorithms with their own gradients, their own hyperparameters, and their own reference implementations, and a sizeable body of empirical work compares them. We show that the gradient of the clipped surrogate is reproduced exactly by a Kullback-Leibler surrogate whose coefficient varies per sample, with closed-form dependence on the importance ratio and the advantage. The identity holds at every minibatch step and across the entire inner loop, and on five MuJoCo continuous-control benchmarks the two losses produce indistinguishable training curves. The reformulation exposes a structural feature of the clipped surrogate that the min notation hides. PPO-Clip's implicit per-sample penalty is a step function at the boundary of the trust region, and the shape of this coefficient is the natural design axis for generalising the algorithm. We sketch the resulting follow-up directions in the discussion.

Riccardo Colletti, Robin Holzinger

University of California, Berkeley

KL-Regularized RL Policy Gradient Methods Proximal Policy Optimization Policy Learning

Jun 20, 2026cs.LG

Drowning in Routine: Signal Dilution in Multi-Turn Agent Training

Multi-turn agents interleave consequential decisions with routine execution: some actions change the downstream return distribution, while others are necessary but reward-equivalent. The cost of trajectory-level credit assignment, often attributed to long horizons, is in fact governed by decision density

ρ

: the fraction of turns whose actions affect the return. When decision density is low, routine turns create signal dilution: they add gradient variance to trajectory-level estimators such as GRPO without adding expected signal. Under explicit assumptions, the resulting turn-level to trajectory-level signal-to-noise ratio scales as

ρ^{-1/2}

, provided critic error remains controlled. The same analysis identifies the complementary regime: at high decision density, trajectory-level methods can remain competitive while avoiding the cost of a critic. In a controlled environment where

ρ

is exactly tunable, the predicted scaling is recovered with

R^2 = 0.999

, and the training-step gap widens significantly as

ρ\to 0

.

Yann Pernot, Vi Retault

Mila - Québec AI Institute · Polytechnique Montréal

Reinforcement Learning Credit Assignment in RL Policy Gradient Methods LLM Agent Training Policy Learning

Jun 19, 2026cs.LG

Backpropagating Through Simulation: Analytic Policy Gradients for Sample and Learning Efficient Differentiable Continuous Control

Model-free reinforcement learning algorithms such as Proximal Policy Optimization (PPO) treat the environment as a black box, estimating policy gradients from sampled rewards; this process demands millions of interactions and relies on high-variance advantage estimates. When environment dynamics are differentiable, the return is an end-to-end differentiable function of the policy parameters, enabling exact gradient computation via backpropagation through simulation. We term this approach Analytic Policy Gradients (APG) and evaluate it against PPO on four continuous control tasks of increasing dynamical complexity: a one-dimensional point-mass target-reaching task, a 2D point-mass navigation task with obstacle avoidance, a 2D rigid-body T-block pushing task, and a 7-DOF Franka FR3 end-effector reaching task. Both algorithms share identical model architectures, observation normalization, and optimizer settings. To decouple sample efficiency from compute efficiency, we design a multi-axis evaluation protocol that records performance against environment steps and gradient steps. We report a segmented backpropagation scheme with MC and critic-based bootstrap modes that mitigates gradient degradation on long-horizon tasks, and present ablations over segment length and bootstrap strategy.

Yueci Deng

School of Data Science, The Chinese University of Hong Kong, Shenzhen

Robotic RL Policy Gradient Methods Continuous Control Policy Learning Sample-Efficient RL

Jun 17, 2026cs.LG

STARE: Surprisal-Guided Token-Level Advantage Reweighting for Policy Entropy Stability

Reinforcement Learning with Verifiable Rewards algorithms like GRPO have emerged as the dominant post-training paradigm for complex reasoning in LLMs, yet commonly suffer from policy entropy collapse during training. We conduct a first-order gradient analysis of token-level entropy dynamics under GRPO and identify a token-level credit assignment mismatch: the per-token entropy variation decomposes into the product of the trajectory-level advantage and an entropy sensitivity function over the next-token distribution, yielding an advantage-surprisal four-quadrant structure and a near-criticality property. Motivated by it, we propose STARE (Surprisal-guided Token-level Advantage Reweighting for policy Entropy stability), which identifies entropy-critical token subsets via batch-internal surprisal quantiles, selectively reweights their effective advantages, and incorporates a target-entropy closed-loop gate for stable entropy regulation. Across model scales from 1.5B to 32B and three task families (Short CoT, Long CoT, and Multi-Turn Tool Use), STARE sustains stable RL training over thousands of steps while maintaining policy entropy within the target band. On AIME24 and AIME25, STARE outperforms DAPO and other competitive baselines by 4%-8% in average accuracy, with reflection tokens and response length growing in tandem, indicating sustained exploration-exploitation balance that further unlocks RL training potential.Code is available at https://github.com/hp-luo/STARE.

Haipeng Luo, Qingfeng Sun, Songli Wu +4

Shenzhen International Graduate School, Tsinghua University · Tencent Hunyuan

RL for Language Model Reasoning Maximum Entropy RL Reinforcement Learning with Verifiable Rewards Policy Gradient Methods

Jun 15, 2026cs.LG

GD $^2$ PO: Mitigating Multi-Reward Conflicts via Group-Dynamic reward-Decoupled Policy Optimization

As LLMs advance, post-training reinforcement learning (RL) increasingly relies on multi-dimensional rewards to cultivate comprehensive capabilities. This shift demands new algorithms capable of optimizing diverse and potentially competing objectives simultaneously. To address this, existing methods such as Group reward-Decoupled Policy Optimization (GDPO) decompose the overall score into independent reward groups, then compute the RL loss separately within each group. However, this strategy still encounters multi-reward conflicts: a single rollout can yield positive advantages on certain reward dimensions but negative ones on others, causing opposing signals to cancel each other out during aggregation, further hindering RL training efficiency. Inspired by Dynamic sAmpling Policy Optimization (DAPO), which improves RL training efficiency by filtering out ineffective rollouts with near-zero advantages, we propose Group-Dynamic reward-Decoupled Policy Optimization (GD

^2

PO). Specifically, GD

^2

PO employs a conflict-aware filtering mechanism to mask out rollouts suffering from severe reward-wise disagreement. By preventing conflicting signals from canceling each other out, this masking strategy preserves and enhances the magnitude of effective RL advantages, thereby significantly accelerating learning efficiency. Furthermore, we introduce query-level reweighting to dynamically adjust the update intensity of each query based on its overall reward consensus. Experiments on various multi-reward scenarios, including tool calling and human preference alignment, demonstrate that GD

^2

PO consistently and significantly outperforms existing baselines. The code is available at https://github.com/Qwen-Applications/GD2PO.

Haotian Liu, Yihao Liu, Jingwei Ni +11

Alibaba · Renmin University of China · Peking University +3

Multi-Objective Reinforcement Learning RL for Language Models Policy Gradient Methods RL Post-Training

Jun 15, 2026cs.AI

A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions

Policy gradient algorithms for language models optimize the same objective

J(θ) = \mathbb{E}*{τ\sim p*θ(τ)}[R(τ)]

, which has exactly two factors: the trajectory probability

p_θ(τ)

and the reward

R(τ)

. Every method from REINFORCE to PPO to GRPO and their descendants modifies one or both factors to address a specific failure in the preceding formulation. Existing surveys organize these methods by domain or chronology, which obscures the rationale behind each design choice and the precise location of its intervention within the gradient estimator. This survey revisits the landscape of LLM policy optimization from

J(θ)

on first principles and uses the trajectory side, induced by

p_θ(τ)

, and the reward side, induced by

R(τ)

, as the two axes along which methods are located. It covers the path from REINFORCE and PPO to GRPO, as well as post-GRPO variants, Agentic RL, and GRPO-OPD. The resulting framework is unified, diagnostic, and extensible: it analyzes methods from a shared objective, identifies which side each method modifies and why, and applies the same trajectory and reward axes across these settings. Across these settings, the framework also exposes compound failures that no single-side fix resolves and that therefore require joint design of the trajectory side and the reward side. The boundary cases and coupled failures identified by this map mark where existing solutions run out and provide a principled starting point for designing the next generation of LLM policy optimization algorithms.

Jianghan Shen, Siqi Luo, Yue Li +9

1Nanjing University · 2Shanghai Artificial Intelligence Laboratory · 3Shanghai Jiao Tong University +4

RL for Language Models Group Relative Policy Optimization Policy Gradient Methods Proximal Policy Optimization Policy Learning

Jun 15, 2026cs.LG

A Gradient Perspective on RLVR Stability and Winner Advantage Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but GRPO-style optimization remains prone to collapse. We analyse this instability through token-level gradient dynamics, deriving a taxonomy that predicts how updates affect next-token probabilities and entropy. The taxonomy shows that stability depends jointly on the advantage sign and token distribution under the current policy. Motivated by this finding, we propose Winner Advantage Policy Optimization (WAPO), a simple online clipped policy-gradient objective that updates only on positive-advantage completions. Across mathematical reasoning and multi-hop QA benchmarks, WAPO improves training stability and matches or outperforms baselines across multiple model families. Full code can be found at https://github.com/layer6ai-labs/wapo.

Prasanth YSS, Zhichen Ren, Rasa Hosseinzadeh +6

Layer 6 AI

RL for Language Model Reasoning Policy Optimization Reinforcement Learning with Verifiable Rewards Policy Gradient Methods

Jun 14, 2026cs.LG

Proximal Policy Optimization for Amortized Discrete Sampling

This paper explores policy gradient algorithms for training stochastic policies to sample from structured discrete probability distributions under the Generative Flow Network (GFlowNet) framework. Building on extensive theoretical connections between GFlowNets and entropy-regularized reinforcement learning, we derive equivalents of standard policy gradient algorithms for training GFlowNets, as well as experimentally explore their various methodological aspects, including baseline training and advantage estimation. Most importantly, our work is the first to derive and successfully apply proximal policy optimization to GFlowNets, showing its improved convergence speed and data efficiency compared to standard GFlowNet training objectives on benchmarks ranging from synthetic energies to molecular graph generation.

Anna Zykova-Myzina, Timofei Gritsaev, Daniil Tiapkin +1

HSE University · Constructor University · CMAP, CNRS, École polytechnique, IPP

Molecular Graph Generation Generative Flow Networks Policy Gradient Methods Proximal Policy Optimization

Jun 11, 2026cs.LG

DiPOD: Diffusion Policy Optimization without Drifting Apart

RL post-training has become increasingly pivotal for improving diffusion policies, but existing diffusion policy-gradient methods are often unstable and cannot achieve reliable policy improvement. We identify the cause as the double-drift phenomenon: optimizing a variational surrogate can let the ELBO separate from the true log-likelihood, which then makes the resulting proxy policy gradient misaligned with the true policy gradient of expected return. We propose \textbf{DiPOD}, a diffusion policy optimization framework that maintains tight-bound behavior throughout training by interleaving self-distillation with policy-improving gradient updates. This leads to a simple and practical algorithm: augmenting each diffusion policy-gradient update with an on-policy ELBO regularizer. Across diffusion language model post-training and continuous-control diffusion policies, DiPOD substantially stabilizes training and reaches higher rewards than previous methods.

Haozhe Jiang, Haiwen Feng, Pieter Abbeel +3

UC Berkeley · NVIDIA

Policy Gradient Methods RL for Diffusion Models Diffusion Language Models

Jun 6, 2026cs.LG

The Easy, the Hard, and the Learnable: Confidence and Difficulty-Adaptive Policy Optimization for LLM Reasoning

RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question difficulty and the model's current competence. Motivated by this, we propose Confidence and Difficulty-adaptive Policy Optimization (CoDaPO), which assigns each question a bounded value from rollout confidence and empirical difficulty. CoDaPO then uses this value to reweight policy updates and resample high-value learnable questions within mini-batches, thereby increasing discovery within the learnable band under a fixed compute budget. Across twelve benchmarks, CoDaPO consistently improves accuracy over existing RL methods. Our code is publicly available at https://github.com/tmlr-group/CoDaPO.

Zhanke Zhou, Xiangyu Lu, Chentao Cao +4

1TMLR Group, Department of Computer Science, Hong Kong Baptist University · 2Stanford University · 3Sydney AI Centre, The University of Sydney

RL for Language Model Reasoning Policy Optimization Reinforcement Learning with Verifiable Rewards Policy Gradient Methods

Jun 5, 2026cs.LG

Generative Modeling of Discrete Latent Structures via Dynamic Policy Gradients

Many scientific problems require inferring unobserved mechanistic latent states from indirect observations. While classical approaches, including expectation maximization, do not scale to combinatorially large spaces, deep learning approaches such as variational autoencoders typically form artificial latent states rather than reconstructing the mechanistic ground-truth states. Here, we introduce GReinSS, a policy learning framework that uses dynamically rescaled rewards to learn latent state distributions that maximize the observed data likelihood. We show that GReinSS accurately reconstructs simulated latent sets and latent graphs, outperforming alternative policy learning and generative modeling baselines. Additionally, GReinSS reconstructs isoforms from real short-read RNA sequencing data that better match isoforms detected by orthogonal long-read sequencing than the standard RSEM algorithm. Overall, GReinSS is a principled and practically effective approach for generative modeling and inference of combinatorial latent states from indirect observations.

Stefan Ivanovic, Ge Liu, Mohammed El-Kebir

Siebel School of Computing and Data Science, University of Illinois at Urbana-Champaign, IL 61801, USA · Cancer Center at Illinois, University of Illinois Urbana-Champaign, IL 61801, USA

Latent Variable Models Policy Gradient Methods RL for Generative Models

Jun 5, 2026cs.LG

GenPO++: Generative Policy Optimization with Jacobian-free Likelihood Ratios

Generative policies provide expressive and multimodal action distributions, making them attractive for reinforcement learning (RL) in complex continuous-control tasks. Among them, flow-based policies are especially appealing because they generate actions through deterministic transport maps. However, applying such generative policies to likelihood-based on-policy learning remains limited by the difficulty of evaluating the probability of executed actions. Existing flow RL methods either replace the true action-density ratio with approximate surrogates, which can introduce biased updates, or recover exact likelihoods through dummy-action augmentation, which enlarges the policy space and increases computation. In this work, we propose GenPO++, a reversible generative policy optimization framework that uses history states as auxiliary memory in a high-order reversible ODE solver, yielding exact inversion without changing the original action dimension. The resulting generative policy map has a log-determinant determined only by fixed solver coefficients, enabling exact and Jacobian-free likelihood-ratio computation. This design preserves the expressiveness of generative flow policies while avoiding both action ratio bias and dummy-action overhead. We evaluate GenPO++ on large-scale simulated control, fine-tuning, and real-world robotic manipulation tasks, where it achieves competitive or superior performance over state-of-the-art on-policy RL methods, while improving training stability and computational efficiency.

Ke Hu, Shutong Ding, Panxin Tao +2

ShanghaiTech University

RL Control Policy Gradient Methods Flow-Based Generative Modeling RL for Generative Models

Jun 4, 2026cs.LG

OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation

Policy-gradient methods usually optimize expected return, but many real world applications care about distributional properties of returns: tail risk, outlier robustness, or best-of-K discovery. We introduce OrderGrad, a family of likelihood-ratio and reparameterization gradient estimators for order-statistic objectives. OrderGrad optimizes finite-sample L-statistics, i.e., weighted averages of sorted rewards or costs, recovering objectives such as VaR, CVaR, trimmed means, medians, and top-m/best-of-K criteria by changing only the rank weights. For any fixed sample size and rank-weight vector, OrderGrad provides an unbiased gradient estimator for the corresponding order-statistic objective. The method is implemented as a simple reward transformation that can then be used in an otherwise standard policy-gradient or reparameterized update. We study the resulting estimator's variance behavior and evaluate it on tasks where mean optimization is mismatched to the deployment objective, including LLM math post-training and other tasks. OrderGrad provides a unified, plug-and-play route to risk-averse, robust, and exploratory learning. Code: https://github.com/paavo5/ordergrad

Paavo Parmas, Yongmin Kim, Kohsei Matsutani +5

The University of Tokyo

Stochastic Optimization Risk-Sensitive RL Policy Gradient Methods RL for Generative Models Policy Learning

Jun 4, 2026cs.LG

On Advantage Estimates for Max@K Policy Gradients

Reinforcement learning with verifiable rewards is widely used for post-training reasoning models, but sparse outcome rewards make exploration difficult. A complementary approach is to optimize inference-time objectives such as pass@K and max@K directly, yet existing policy-gradient estimators for these objectives use different signals, baselines, and normalizations, making their relationships unclear. We study this issue through baseline design and advantage centering. Starting from the advantage estimator of a leading method in the field, we show that it is policy-gradient unbiased but yields a non-centered advantage. We then introduce a Leave-Two-Out baseline that preserves policy-gradient unbiasedness while making realized batch advantages exactly centered. The resulting method, MaxPO, has an efficient quadratic-time implementation and integrates naturally into group-based RL for LLM post-training. We further derive the canonical finite-batch advantage for max@K, providing a unified view of existing advantage estimators. Empirically, we verify that the L2O baseline reduces gradient variance and outperforms non-centered alternatives.

Shota Takashiro, Soichiro Nishimori, Paavo Parmas +6

The University of Tokyo

Policy Gradient Policy Gradient Methods RL Post-Training Policy Learning

Jun 4, 2026cs.AI

Retry Policy Gradients in Continuous Action Spaces

Retry-based objectives such as pass@K and max@K optimize the best return obtained from multiple sampled trajectories, and recent work has shown that they can promote exploration without explicit exploration bonuses. In discrete action spaces, ReMax was shown to do so by adapting to return uncertainty. In this work, we introduce pathwise derivative estimators for retry objectives and use them to extend ReMax to continuous action spaces. We study the resulting learning dynamics and show that, even with deterministic rewards, ReMax can encourage stochastic exploration by reshaping the policy-gradient landscape. In particular, it alters gradients both in direction, biasing updates toward higher policy entropy, and in magnitude, damping gradients and slowing convergence. We further show that Adam's adaptive normalization can mitigate this damping, depending on its numerical stabilization parameter. Empirically, we instantiate this objective as ReMax Actor-Critic (ReMAC), an off-policy actor--critic algorithm that optimizes the ReMax objective using a pathwise derivative estimator. Our experiments show that ReMAC can promote higher policy entropy without entropy regularization and achieves performance comparable to SAC.

Soichiro Nishimori, Paavo Parmas

The University of Tokyo, Japan

Policy Optimization RL Exploration Policy Gradient Methods Actor-Critic Methods Policy Learning

Jun 4, 2026cs.LG

When Denser Credit Is Not Enough: Evidence-Calibrated Policy Optimization for Long-Horizon LLM Agent Training

Long-horizon LLM agents require reinforcement learning methods that can assign credit to intermediate decisions under sparse and delayed rewards. Recent group-based methods such as GiGPO improve over GRPO by constructing step-level advantages at repeated anchor states. However, we show that such dense credit can be statistically unreliable: under limited rollouts, rare but lucky actions may receive overly large advantages, producing divergent anchor bias and late-stage training oscillation. We propose Evidence-Calibrated Policy Optimization (ECPO), a critic-free policy optimization algorithm that calibrates step-level credit before policy updates. ECPO combines Evidence-Calibrated Action Advantage, which groups rollouts by canonical actions and shrinks low-count estimates, with Variance-Gated Credit Weighting, which suppresses anchor states dominated by within-action noise. Experiments on ALFWorld and WebShop with Qwen2.5-1.5B/7B show that ECPO consistently outperforms strong baselines, improving GiGPO by +5.2/+7.3 success points on ALFWorld/WebShop with Qwen2.5-1.5B while adding only 0.1% additional advantage-computation overhead.

Yuanfan Li, Qi Zhou, Wenjing Duan +1

X-LANCE Lab, School of Computer Science, Shanghai Jiao Tong University, Shanghai, China · Faculty of Electronic and Information Engineering, Xi’an Jiaotong University

Credit Assignment in RL Step-Level Credit Assignment in RL Policy Gradient Methods Sparse-Reward RL Policy Learning RL for LLM Agents

Jun 3, 2026cs.LG

Policy Gradient for Continuous-Time Robust Markov Decision Processes

The framework of robust Markov decision processes (RMDPs) allows the design of reinforcement learning agents that satisfy performance guarantees under worst-case transition dynamics. Traditional RMDPs consider discrete-time dynamics and recently, sample-efficient policy gradient algorithms have been considered in this context. This paper investigates policy gradient algorithms within a continuous-time RMDP framework. Policy gradients and adversarial gradients are derived using pathwise and adjoint-based formulas for stochastic and ordinary differential equations. We propose double-loop optimisers to obtain linear convergence in the oracle-based setting and an

\tilde{\mathcal{O}}(\frac{1}{ε^2})

sample complexity in the sample-based setting in an analysis which also derives novel tools for the framework of undiscounted total cost MDPs. Additionally, we propose mean-field optimisers as distributional optimisers with an

\tilde{\mathcal{O}}(\frac{1}{K})

oracle-based convergence rate and an

\tilde{\mathcal{O}}(\frac{N^2}ε)

sample complexity under

N

-particle approximation. The effectiveness of continuous-time policy gradient algorithms is confirmed for both optimisers on continuous-time RMDPs with neural ordinary differential equation dynamics.

Tanya Veeravalli, David M. Bossens, Atsushi Nitanda

Centre for Frontier AI Research, Agency for Science, Technology and Research (A*STAR) · Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR) · College of Computing and Data Science, Nanyang Technological University

Robust Markov Decision Processes Markov Decision Processes Continuous-Time RL Policy Gradient Methods Robust RL Policy Learning

Jun 2, 2026cs.LG

Local Guidance, Global Impact: Gaussian-Reshaped Trust Region Unlocks Behavior Transitions

While Proximal Policy Optimization (PPO) demonstrates strong performance in stationary settings, we show that its standard optimization paradigm struggles in continual and non-stationary environments. The failure does not stem from insufficient model capacity or overly restrictive clipping. Instead, PPO performs persistent, directionally inefficient local updates, which indicates a lack of geometry-aware guidance for accumulating meaningful behavioral change and ultimately hindering transitions toward new behavior patterns. Although divergence-based regularization introduces partial geometric awareness, its monotonically increasing penalties implicitly discourage large policy deviations, even when such shifts are necessary for effective adaptation. To address this limitation, we propose Gaussian Trust Region Policy Optimization (GTR), which reshapes the trust region using a Gaussian kernel. The resulting constraint is bounded and non-monotonic, providing strong local stability while progressively relaxing under sustained high-advantage updates. To further improve robustness, we introduce a Mixture Gaussian Anchor that adapts to recent policy trajectories, reducing variance induced by stale references. GTR is architecture-agnostic and achieves strong performance across games, simulated robotic control, open-world exploration, and language model post-training. These results demonstrate that geometry-aware trust-region design can be a promising direction for robust reinforcement learning in complex non-stationary environments. Our code is available at https://anonymous.4open.science/r/GTR_demo/README.md.

Bingxu Liu, Jiashun Liu, Johan Obando-Ceron +5

Hong Kong University of Science and Technology · Fudan University · Mila - Québec AI Institute +2

Non-Stationary RL Reinforcement Learning Policy Gradient Methods Proximal Policy Optimization Trust Region Policy Optimization Robust RL

Jun 2, 2026cs.LG

Self-Distilled Policy Gradient

On-policy self-distillation, where a language model conditions on privileged context to supervise its own generations, is a promising source of dense supervision for sparse-reward reinforcement learning. Actually, it can be instantiated as an auxiliary full-vocabulary student-to-teacher reverse Kullback-Leibler divergence loss. We therefore propose SDPG, a self-distilled policy-gradient framework that combines group-relative verifier advantages with normalized standard deviation, exact full-vocabulary on-policy self-distillation, as well as reference-policy KL regularization. Empirically, SDPG improves stability and performance over RLVR and self-distillation baselines. The code is available at https://github.com/lauyikfung/SDPG.

Yifeng Liu, Shiyuan Zhang, Yifan Zhang +1

Department of Computer Science, University of California, Los Angeles, CA, USA · Princeton AI Laboratory, Princeton University, Princeton, NJ, USA

Policy Gradient On-Policy Self-Distillation Reinforcement Learning with Verifiable Rewards Policy Gradient Methods

Jun 1, 2026cs.LG

Task-Induced Representational Invariances Depend on Learning Objective in Deep RL

Reinforcement Learning (RL) has long served as a model for goal-directed animal behavior in neuroscience. Modern deep RL has shown remarkable success across many domains, further strengthening this connection. The ability to learn abstract representations of high-dimensional state spaces underlies much of this success. However, theoretical understanding of these learned representations remains limited, hindering direct comparisons between models and animal learning. We address this gap by analyzing deep RL representations through the lens of MDP reduction theory. Investigating canonical RL algorithms in a navigation task, we find that even when performance is comparable, the value-based method (DQN) learns representations that are invariant to MDP homomorphism symmetries, while the policy-gradient method (PPO) learns representations invariant to action symmetries. These differences emerge consistently across domains, have downstream consequences for transfer learning, and appear in LLMs in a prompt-dependent manner. Our findings provide a principled approach to comparing learned representations across RL algorithms, with demonstrated practical implications and possible insights for neural coding in the brain.

Manu Srinath Halvagal, Sebastian Lee, SueYeon Chung

Department of Physics, Harvard University · 2Kempner Institute, Harvard University · Center for Computational Neuroscience, Flatiron Institute

Markov Decision Processes Deep Q-Learning Policy Gradient Methods State Representation Learning Invariant Representation Learning

May 31, 2026cs.LG

Decision-Focused On-Policy Learning for Contextual Linear Optimization with Partial Feedback

Decision-focused learning (DFL) trains predictive models by optimizing downstream decision quality rather than standalone prediction accuracy. For contextual linear optimization, most existing DFL methods assume offline data and full observations of the objective cost vector. We develop an on-policy learning method for sequential contextual linear optimization under partial feedback, generalizing the standard bandit feedback setting. Our method learns a stochastic predict-then-optimize policy that samples a cost-vector prediction from a conditional distribution and solves the resulting downstream linear optimization problem. To update this distributional model, we introduce a two-component hybrid gradient estimator. The first component is a score function estimator, which provides an unbiased but potentially high-variance policy gradient estimate. The second is a decision-focused plug-in component that uses an auxiliary nuisance estimate of the latent cost vector to exploit the downstream optimization structure, becoming more informative as the estimate improves. We prove an O(T^-1/2) bound on the average squared policy-gradient norm, matching the standard non-convex SGD rate. Experiments on top-k selection, shortest path, combinatorial pricing, and a real-data energy-scheduling benchmark show that, under bandit feedback, the hybrid gradient approach achieves lower mean cumulative regret than the contextual-bandit baselines on all four benchmarks and than linear Thompson sampling on three, and that it also works with richer conditional generative cost models. Code is available at https://github.com/Joeyetinghan/on-policy-bandit-dfl.

Wyame Benslimane, Tinghan Ye, Pascal Van Hentenryck +1

Department of Industrial Engineering and Operations Research University of California, Berkeley · H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology

Predict-Then-Optimize Decision-Focused Learning Policy Gradient Methods Contextual Bandits Policy Learning

May 31, 2026cs.LG

OPD+: Rethinking the Advantage Design for On-Policy Distillation

On-policy distillation (OPD) is a widely used technique to transfer capabilities from capable teacher language models to the base student models, and can be formulated in a reinforcement learning style objective using student generated rollouts. Yet, despite the divergence reward being dependent on student model likelihood, existing works usually adopt a stop gradient design primarily for stability, which makes the resulting advantage estimation questionable. In this work, we provide a generic optimization framework based on f-divergence between the student and teacher, and mathematically revisit whether such design space is valid. We prove that general stop-gradient operation would lead to biased estimates of the reward objective and corresponding gradient for general divergence functions. We propose OPD+, the corrected version of OPD that demonstrates improved performance over the baseline KL approach and also supports the choice of various f-divergence. We validate our findings on mathematical reasoning and tool-use benchmarks.

Hanyang Zhao, Haoxian Chen, Han Lin +3

Columbia University · Amazon · Meta +1

Language Model Distillation Policy Gradient Methods On-Policy Distillation Teacher-Student Learning

May 29, 2026cs.LG

Zero Collapse: A Failure Mode of Policy Gradient Methods in Discontinuous Reward Environments

Bidding in repeated auctions is a central challenge for reinforcement learning (RL), combining continuous control with the strategic complexities of digital advertising. While policy gradient and value-based methods seem well-suited for these settings, they often struggle with the discontinuous, "cliff-like" nature of auction reward landscapes. In a first-price auction, for example, a bidder receives zero reward until they cross a specific threshold, after which the reward decreases as the bid increases. This creates a landscape of flat, zero-reward regions separated by sharp boundaries. We identify a fundamental failure mode in this setting termed "zero collapse." We show that stochastic exploration and gradient-based updates can cause policies to overshoot optimal high-reward regions and enter flat, zero-reward regimes. Once there, the lack of an informative gradient signal makes recovery extremely sample-inefficient, effectively trapping the agent. We find that actor-critic methods are particularly susceptible, as biased value estimates can accelerate this movement toward unstable regions. Our contributions include: (1) a mechanistic explanation of how discontinuous rewards lead to vanishing signals and zero collapse; (2) an analysis of the interaction between policy stochasticity and step size; and (3) an empirical demonstration of this phenomenon across REINFORCE and actor-critic variants. We propose practical mitigation strategies involving initialization and architectural choices to improve stability. Finally, we introduce a formal RL framework for auction environments highlighting their unique structural properties.

Nishant Kumar, Enrique Areyan Viqueira, Amy Greenwald

Reinforcement Learning Policy Gradient Methods Actor-Critic Methods

May 29, 2026cs.LG

Emergence of Exploration in Policy Gradient Reinforcement Learning via Retrying

In reinforcement learning (RL), agents benefit from exploration only because they repeatedly encounter similar states: trying different actions can improve performance or reduce uncertainty; without such retries, a greedy policy is optimal. We formalize this intuition with ReMax, an objective that evaluates a policy by the expected maximum return over

M

samples, where

M

is a positive integer, while accounting for return uncertainty. Optimizing this objective induces stochastic exploration as an emergent property, without explicit bonus terms. For efficient policy optimization, we derive a new policy-gradient formulation for ReMax and introduce ReMax PPO (RePPO), a PPO variant that optimizes ReMax while generalizing the discrete retry count

M

to a continuous parameter

m > 0

, enabling fine-grained control of exploration. Empirically, RePPO promotes exploration, without any explicit exploration bonuses, on the MinAtar and Craftax benchmarks.

Soichiro Nishimori, Paavo Parmas, Sotetsu Koyamada +4

The University of Tokyo, Tokyo, Japan · Kobe University, Kobe, Japan · Kyoto University, Kyoto, Japan +3

RL Exploration Policy Gradient Methods Proximal Policy Optimization Policy Learning

May 28, 2026cs.CV

Guidance Contrastive Token Credit Assignment for Discrete Policy Optimization

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level rewards introduces a key limitation as uniform credit assignment across all tokens fails to capture fine-grained, token-level contributions. To address this issue, we propose Guidance Contrastive Policy Optimization (GCPO), a novel algorithm that enables per-token credit assignment by contrasting model predictions under positive and negative prompts. Rather than uniformly broadcasting sample-level advantages, GCPO assigns token-level advantages proportional to the difference between these contrastive predictions, allowing more precise and informative learning signals. Empirically, we find that GCPO emphasizes semantically relevant regions such as visual areas aligned with textual prompts in text-to-image generation, and critical keywords within reasoning traces for chain-of-thought tasks. Through extensive experiments, GCPO consistently outperforms GRPO and DAPO baselines on both text-to-image generation and chain-of-thought reasoning benchmarks, demonstrating its effectiveness as a general and scalable optimization strategy for discrete policy learning.

Shufan Li, Konstantinos Kallidromitis, Akash Gokul +2

UCLA · Panasonic AI Research · NVIDIA

Token-Level Credit Assignment RL for Language Model Reasoning Credit Assignment in RL Policy Optimization RL for Image Generation Policy Gradient Methods

May 27, 2026cs.AI

Modeling Vehicle-Type-Specific Pedestrian Crash Avoidance Behavior in Safety-Critical Interactions Using Smooth-Mamba Deep Reinforcement Learning

As automated vehicles (AVs) increasingly share roadways with human-driven vehicles (HDVs), understanding how pedestrians respond to different vehicle types in safety-critical interactions is essential for the safe deployment of automated driving technologies. This study extracts safety-critical pedestrian-vehicle interactions from the Argoverse 2 dataset to capture real-world crash avoidance behaviors in encounters involving AVs and HDVs. To model vehicle-type-specific pedestrian crash avoidance behavior, we develop a Smooth-Mamba Deep Deterministic Policy Gradient framework, termed SMamba-DDPG, which integrates smooth action constraints with efficient temporal representation learning. To quantify pedestrian behavioral differences, the framework trains separate crash avoidance policies for pedestrian interactions with AVs and HDVs. Results show that SMamba-DDPG outperforms baseline reinforcement learning and supervised learning models in reproducing pedestrian crash avoidance behaviors. Reconstructed trajectories demonstrate strong behavioral realism, accurately reproducing crash avoidance kinematics in both AV and HDV scenarios. Reaction time analysis shows that the model captures human-like response delays and reveals that pedestrians respond more quickly to AVs than to HDVs. Counterfactual analysis further indicates that pedestrians adopt lower crossing speeds when interacting with AVs. Large-scale safety analysis of model-generated data revealed that pedestrian-AV interactions consistently yielded lower conflict rates and higher pedestrian yielding rates compared to pedestrian-HDV interactions. The findings highlight the importance of incorporating vehicle-type-specific pedestrian behavioral models for safer automated driving system design and more realistic traffic simulations in mixed-traffic environments.

Qingwen Pu, Kun Xie, Hong Yang +2

Transportation Informatics Lab, Department of Civil and Environmental Engineering, Old Dominion University, Norfolk, VA 23529, United States · Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA, United States · Department of Transportation and Urban Infrastructure Studies, SMARTER Center, Morgan State University, 1700 E Cold Spring Ln, Baltimore, MD 21251, USA

Collision Avoidance Pedestrian Behavior Modeling Human Behavior Simulation Policy Gradient Methods Deep Deterministic Policy Gradient Autonomous Driving Simulation

May 27, 2026cs.LG

ProRL: Effective Reinforcement Learning for Proactive Recommendation via Rectified Policy Gradient Estimation

Proactive Recommender Systems (PRSs) aim to guide user preference shift toward target items by generating paths of intermediate recommendations. Reinforcement learning (RL) provides a principled framework for optimizing such sequential decision tasks, as path rewards can naturally capture both short-term acceptance and long-term guidance effectiveness. However, naively applying policy gradients to PRS results in deficient gradient estimation. We identify two deficiencies: (1) path-level rewards decompose into step-level rewards with positive mean, creating a length-dependent bias that causes gradients to favor path extension over meaningful exploration; (2) weighting each step by the entire path-level reward ignores the decomposition structure, leading to high gradient variance. To rectify these two deficiencies, we propose an effective RL framework ProRL with two novel mechanisms for proactive recommendation. First, Stepwise Reward Centering subtracts expected rewards to neutralize length-dependent bias, ensuring that path extension yields zero expected gradient signal. Second, Position-Specific Advantage Estimation leverages the reward decomposition structure to compute step-dependent baselines, reducing gradient variance. Together, these mechanisms yield policy gradients that precisely target path quality. Our experiments on three real-world datasets demonstrate that ProRL significantly outperforms state-of-the-art PRSs. Our code is available at https://github.com/hongruhou89/ProRL.

Hongru Hou, Tiehua Mei, Denghui Geng +5

Policy Gradient Methods Recommender Systems

May 26, 2026cs.LG

BASIS: Batchwise Advantage Estimation from Single-Rollout Information Sharing for LLM Reasoning

Reinforcement learning with verifiable rewards has become a standard recipe for improving the reasoning abilities of large language models. Existing algorithms face a tradeoff between computational efficiency and sample efficiency in value estimation and policy learning. We introduce BASIS, a critic-free post-training algorithm designed to address this tradeoff. At each online training step, BASIS samples only one rollout per prompt, but leverages rich information across prompts in the entire batch to improve value function estimation. Our experiments demonstrate that BASIS reduces MSE in value function estimation by 69% compared to REINFORCE++, a representative single-rollout baseline, and achieves lower MSE with one rollout than group mean estimators with 8 rollouts. This improvement in value estimation translates to better policy optimization: using substantially less training time, BASIS achieves performance close to multi-rollout GRPO-type baselines and often outperforms single-rollout REINFORCE-type baselines.

Shijin Gong, Erhan Xu, Kai Ye +3

School of Management, University of Science and Technology of China · Department of Statistics, London School of Economics and Political Science · Department of Engineering Science, University of Oxford

RL for Language Model Reasoning Critic-Free RL Reinforcement Learning with Verifiable Rewards Policy Gradient Methods RL Post-Training Policy Learning+1

May 26, 2026cs.LG

Bilevel Optimization over Saddle Points of Zero-Sum Markov Games

Reinforcement learning (RL) often has a hierarchical structure, where an upper-level (UL) learner selects model parameters and a lower-level (LL) decision-making process responds, naturally leading to a bilevel optimization problem. Most existing bilevel RL methods assume a single-policy LL Markov decision process (MDP), and therefore fail to capture competitive structures arising in applications such as incentive design, where multiple policies interact. We study bilevel optimization problems in which the LL problem is a regularized min-max zero-sum Markov game and the UL objective is optimized through the saddle-point equilibrium induced by the LL game. In this work, we propose penalty-augmented Nikaido-Isoda descent-ascent (PANDA), a penalty-based first-order policy-gradient method based on the Nikaido-Isoda function. By exploiting the min-max game structure, PANDA avoids computing UL hypergradients and does not require second-order information. We prove that PANDA converges to stationary points without convexity assumptions on either the UL or LL objectives. Moreover, PANDA reaches an

ε

-stationary point in

\tilde{\mathcal{O}}(ε^{-1})

iterations with sample complexity

\tilde{\mathcal{O}}(ε^{-3})

, matching the best-known rates for bilevel RL with single-policy LL MDPs. Experiments demonstrate the superior performance of PANDA over closely related baselines.

Zihao Zheng, Irwin King, Songtao Lu

Department of Computer Science and Engineering, The Chinese University of Hong Kong · Shun Hing Institute of Advanced Engineering, The Chinese University of Hong Kong

Game Theory Zero-Sum Games Min-Max Optimization Bilevel Optimization Policy Gradient Methods