Actor-Critic Methods

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9 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 62

Oct 7, 2026cs.LG

A Closed-Loop Non-Asymptotic Convergence Analysis of PPO with Learned Critics and Clipping

Despite its widespread use, Proximal Policy Optimization with clipping (PPO-Clip) remains difficult to tune, and the interactions among critic learning, clipping, and rollout reuse remain incompletely understood. We develop a \emph{non-asymptotic} analysis of PPO-Clip as a \emph{closed-loop actor--critic} system. It captures actor--critic coupling, nonsmooth probability-ratio clipping, finite-batch reuse, and predictable early stopping under explicit coverage and critic regularity assumptions, using raw GAE and Monte Carlo critic targets. Our synchronous and asynchronous guarantees jointly characterize policy stationarity and the tracking accuracy of the learned critic, with explicit dependence on algorithmic parameters. A sufficient coupling condition gives optimization, critic tracking, clipping, and finite-batch errors a common amplification bound. The asynchronous result also requires a delay-dependent critic stepsize restriction; violating these conditions does not establish divergence. For finite layered MDPs with tabular critics, a uniform bound on the actual clipped-gradient class replaces complete-trajectory counting. A verified growing-horizon family has polynomial sample complexity, and a two-time-scale schedule gives

O(T^{-2/5})

stationarity and critic-tracking bounds with explicit fresh-rollout accounting. These results together advance our understanding about PPO and provide theoretical guidance in tuning.

Junwei Su, Mengfan Liu, Yanyong Zhang +1

School of Artificial Intelligence and Data Science, University of Science and Technology of China · Department of Computer Science, University of Hong Kong

Proximal Policy Optimization Actor-Critic Methods Policy Gradient Methods Sample-Efficient RL Asynchronous RL

Oct 6, 2026cs.LG

Foundation Model-Aided Multi-Agent Reinforcement Learning for Wireless Random Access Network Optimization

Random access (RA) is one of the most foundational medium access control (MAC) layer scheduling schemes for handling unpredictable data traffic from multiple terminals. While multi-agent reinforcement learning (MARL) has been explored to optimize RA-based wireless networks, its reliance on experience-driven, distributed policy learning incurs significant training overhead for each optimization task, limiting its feasibility in real-world applications. In this work, we propose to leverage a foundation model (FM) to improve MARL efficiency across diverse RA network optimization tasks. Specifically, we design an FM-aided actor-critic algorithm within a consensus-based decentralized MARL architecture and provide its convergence analysis under local reward exchanges and nonlinear value function approximations to show that our algorithm achieves the same convergence order as the conventional MARL with critic model exchanges and linear approximations. Our numerical results show that our FM-based approach significantly enhances MARL speed for RA network optimization.

Myeung Suk Oh, Zhiyao Zhang, Alvaro Velasquez +2

The Ohio State University Columbus, Ohio, USA · University of Colorado Boulder Boulder, Colorado, USA · Pathfinder Applied Research, LLC Ashburn, Virginia, USA

Wireless Resource Allocation Decentralized MARL Actor-Critic Methods Multi-Agent Reinforcement Learning

Oct 4, 2026stat.ML

Taylor Representations for Model-Free RL in Networked MDPs

In Networked Markov Decision Processes, transition dynamics are often unknown and the state--action space grows rapidly with the number of agents. In this setting, Taylor representations naturally approximate

Q

-functions, but a naive order-

n

expansion over

N

agents requires

Θ(N^n)

coefficients. We justify these expansions under smooth expected future local rewards with controlled derivatives. Under this condition, finite-speed information propagation and discounting imply that local-critic Taylor coefficients decay exponentially with the graph distance to the farthest agent involved. Discarding distant-agent coefficients and marginalizing then yield scalable local Taylor representations with a bound controlled by graph locality. Building on these representations, we propose a scalable model-free actor--critic algorithm, establishing finite-sample critic and near-stationarity guarantees for a linear LSTD critic. We then introduce a more expressive neural TD parameterization. Unlike prior constructive spectral methods, our approach covers settings without access to a known local dynamics map, such as hidden switched linear--quadratic regulation. Across three control benchmarks, our method matches or outperforms spectral baselines while scaling efficiently to large graphs.

Salah Chikhi, Abdelhaq Chaoui, Asuman Ozdaglar +1

Massachusetts Institute of Technology

Markov Decision Processes Representation Learning for RL Model-Free RL Decentralized MARL Actor-Critic Methods

Oct 1, 2026cs.MA

After Cooperation Is Learned: Gradient Routing and Optimizer-Dependent Maintenance in Multi-Agent Reinforcement Learning

Cooperative MARL is commonly evaluated through cooperation discovery from random initialization, leaving open whether continued optimization can destabilize learned cooperation. Actor-critic comparisons can also conflate critic presence with value gradients entering shared actor representations. We study cooperation maintenance, defined as the survival of a behaviorally verified cooperative policy under continued training. We formulate maintenance as a right-censored event-time problem and compare matched warm starts: X0 allows value loss gradients to update shared actor features, X1 retains the critic while blocking those gradients, and X5 removes the learned critic as a critic-free reference. This isolates direct value-gradient access while controlling initialization, critic computation, and evaluation. Positive reward scaling preserves strategic preferences and equilibria while perturbing learning dynamics. Gradient audits confirm the intended routing pathways, and frozen-policy torso perturbations probe whether route-induced updates align with local cooperation boundaries. In confirmatory MinEx and CleanUp-lite experiments, higher scales selectively increase maintenance sensitivity in X0; X1 remains near the censoring ceiling, and X5 has no confirmed events in the tested settings. In CleanUp-lite, route-by-scale displacement is associated with reduced local cooperation margins; MinEx shows a weaker, optimizer-dependent effect. These results identify a conditional, scale-sensitive maintenance risk associated with direct value-gradient routing rather than a universal failure of critics.

Chaoyuan Hao, Wentao Yue, Tianyou Lai +4

Actor-Critic Methods Cooperative MARL

Sep 30, 2026cs.LG

Trust the Critic More

Standard language model RL algorithms credit every token of a long rollout with the same advantage determined by the terminal reward. Actor-critic methods can provide finer-grained credit assignment, but learned critics are generally considered too inaccurate to trust when training LLMs with RL. In recent works, even when a critic is present, it is used only for baseline estimation, so every trajectory must be rolled out to its terminal reward. We introduce Actor-Critic with Action Chunking (AC2) that removes the need to roll every trajectory to completion. AC2 instead assigns credit to action chunks: short continuations of prefixes of past trajectories. A learned critic scores the state reached at the end of each action chunk, allowing the policy to update without observing a terminal reward. We make critic-based credit assignment reliable through three design choices. First, we introduce local readiness which uses critic-based updates on a problem only when the critic is sufficiently accurate on that particular problem. Second, when available, we provide the critic with a reference solution from a previous successful rollout. Third, we assign credit over action chunks of 10k tokens rather than individual tokens, giving the critic a more meaningful portion of the trajectory to evaluate. We train Qwen3-4B on FineProofs-RL using AC2 and evaluate on IMO-ProofBench. AC2 exceeds GRPO's peak validation score of 18.5% using 2.5x fewer decoding FLOPs. This gain comes from two sources, (1) AC2 requires 25% fewer training steps to reach this score, and (2) each step generates fewer tokens because the policy does not need to continue every trajectory to completion. Conceptually, we demonstrate that we can remove the need to roll out every trajectory to completion, opening up a large previously unexplored design space for LLM RL algorithms.

Kaiyue Wen, Luke Bailey, Arvind Mahankali +1

Stanford University

RL for Language Model Reasoning Credit Assignment in RL RL Post-Training Action Chunking Actor-Critic Methods

Sep 30, 2026cs.LG

DAMPER: Return-Prioritized Gradient Control for Smooth Policies

Actor-critic methods achieve strong performance in continuous control, but their policies can produce highly oscillatory actions. A common remedy is to add auxiliary smoothness losses. However, their contribution can be negligible when their gradients are small relative to the native actor gradient. Moreover, existing methods often combine multiple auxiliary losses, complicating loss balancing without necessarily improving the return-smoothness trade-off. We introduce DAMPER (Direction-Aware Magnitude-Controlled Projection with Explicit Return Priority), which combines the native actor gradient with a temporal-consistency gradient through conflict-conditioned projection and adaptive magnitude control. It removes the auxiliary component opposing the actor gradient and scales the retained temporal direction relative to the actor gradient norm, preserving positive alignment with the native actor gradient. Experiments with TD3 and SAC on six continuous-control tasks show reduced action oscillation relative to the native agents in all 12 task-backbone pairs and the best oscillation score among the compared methods in eight, with task-dependent return trade-offs.

Seokmin Ko, Taewon Goo, Kihyuk Hong

KAIST

RL Control Reinforcement Learning Gradient Interference Actor-Critic Methods Policy Learning

Sep 29, 2026cs.LG

Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR

Assigning credit to intermediate steps remains a central challenge in training Large Language Models (LLMs) on multi-step reasoning tasks with sparse terminal rewards, and actor-critic methods such as PPO address this by learning value functions to construct token-level advantages. Their effectiveness, however, hinges on reliable value estimation, a difficult task requiring the critic to both assess progress toward a correct solution and anticipate an evolving policy's future behavior; errors in either can compromise credit assignment and destabilize online training. In this paper, we revisit the standard state-only formulation of value estimation and propose

π

PPO, a self-privileged actor-critic framework. By reusing verified same-prompt rollouts as contrastive evidence,

π

PPO helps the critic assess intermediate reasoning against successful and failed attempts, while preserving standard policy optimization and the deployment interface. Experiments show that

π

PPO consistently improves value-estimation quality by a substantial margin and outperforms representative actor-critic and critic-free RLVR baselines on challenging mathematical reasoning benchmarks, while remaining effective even when paired with substantially smaller asymmetric critics.

Kun Liang, Chenming Tang, Clive Bai +5

School of Computer Science, Peking University · National Key Laboratory for Multimedia Information Processing, Peking University · Foundation Model Department, Tencent

Value Function Estimation RL for Language Model Reasoning Credit Assignment in RL Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Actor-Critic Methods+1

Sep 24, 2026cs.LG

A Concentration Bound for Two-Timescale Actor-Critic Algorithm

Significant research effort has been directed in recent years towards establishing both asymptotic and non-asymptotic convergence guarantees for two-timescale actor--critic algorithms, where the actor recursion is run on a slower timescale than the critic recursion. This work derives a uniform all-time concentration bound for the actor--critic algorithm with function approximation in the long-run average-reward setting. This bound helps us analyze the behavior of the actor parameter with high probability. We show that, after some finite time, the actor parameter enters a safe region and remains within it thereafter with high probability. Specifically, with probability at least

1-ε_1-ε_2

, the actor error

\Vert θ_k-θ^{*}\Vert

is

O\left(\frac{n_0^{3/4}}{k}\frac{1}{\sqrt{ε_2}}+\left(\frac{1}{n_0}\right)^{1/4}\log^{1/4}\left(\frac{1}{ε_1}\right)+\left(\frac{1}{n_0}\right)^{1/4}\right)

for all

k\geq n_0

and sufficiently large

n_0

. We also present experimental results demonstrating that the aforementioned actor error diminishes with the number of actor-parameter updates.

Prashansa Panda, Shalabh Bhatnagar

Department of Computer Science and Automation IISc Bangalore

Average-Reward RL Two-Timescale Stochastic Approximation Actor-Critic Methods

Sep 22, 2026cs.LG

PACT: From Credit Assignment to Critic Alignment

Reinforcement learning has become a central component of large language model (LLM) post-training, yet token-level credit lacks a generally accepted mathematical definition, leaving its relationship to commonly used training signals unclear. We formulate three regularity conditions, namely Completeness, Prefix Consistency, and Neutrality, and prove that they uniquely determine token-level credit. This characterization provides a unified basis for explaining phenomena across existing algorithms and guides the development of an improved actor-critic training procedure. Through this lens, an ideal teacher in On-Policy Distillation (OPD) acts as an implicit critic, yielding an expected policy gradient proportional to that induced by token-level credit. Response-level REINFORCE Leave-One-Out (RLOO) signals match the expected policy-gradient contribution of token-level credit despite their coarser granularity. We further establish approximate credit sparsity under bounded outcome rewards and show how intermediate critic errors in Generalized Advantage Estimation (GAE) can become comparable to the underlying credit. These motivate Policy Aligned Critic Training (PACT), which adopts an Actor-then-Critic update order to apply importance sampling correction to critic training and better align the critic with the updated policy. In agentic mathematical reasoning, PACT achieves 72.87% average accuracy across four benchmarks, outperforming GRPO and PPO by 8.80 and 13.16 percentage points, respectively. On SWE-bench Verified, PACT achieves a pass rate of 67.4%, outperforming PPO, GRPO, and SAO by 2.4, 2.0, and 3.8 percentage points, respectively.

Jiayan Fu, Hang Xu, Yong Zhang +4

AllSpark Team

Reinforcement Learning Token-Level Credit Assignment RL for Language Model Reasoning Step-Level Credit Assignment in RL RL Post-Training Actor-Critic Methods+1

Sep 22, 2026cs.LG

Fully Byzantine-Resilient Multi-Agent Reinforcement Learning

We study distributed Byzantine-resilient actor-critic multi-agent reinforcement learning (AC-MARL), where agents collectively learn policies through local interactions. Existing methods guarantee convergence of the agents' parameters only to a neighborhood of the attack-free limit points, resulting in degraded performance. We propose Fully Resilient AC-MARL (FRAC-MARL), a decentralized method in which each agent leverages redundancy in two-hop messages to identify reliable messages. Under linear parameterizations of the value and team-reward functions and Byzantine edge attacks, where adversarial behavior is confined to the communication layer, we prove that agents' parameters converge almost surely to the same limit points as in the attack-free case over time-varying communication graphs. We introduce a novel topological condition for the convergence of our method, present a systematic method to construct such networks, and prove that this condition can be verified in polynomial time. Finally, we demonstrate our method on cooperative multi-robot formation control tasks.

Haejoon Lee, Dimitra Panagou

Robotics Department, University of Michigan, Ann Arbor, MI, USA

Decentralized MARL Actor-Critic Methods Cooperative MARL Multi-Agent Reinforcement Learning

Sep 17, 2026cs.LG

CARE-VI: Conservative Adaptive Reliability Estimation for Value Improvement in Off-Policy Actor-Critic Learning

Reliable temporal-difference targets are central to off-policy actor-critic learning. Direct value improvement refines the next-state target with alternative actions, but the reliability of this refinement depends on how candidate actions are ranked, reviewed, and weighted. Noisy rankings may force premature candidate commitment, reusing selection scores may bias target valuation, and fixed enhancement weights may amplify weak evidence. To address these risks, we develop Conservative Adaptive Ranking and Screening (CARS), which retains an ordered candidate prefix within a preset budget and narrows it only when the observed boundary gap exceeds a disagreement-scaled uncertainty radius. Selector-Evaluator Value Assessment (SEVA) uses selector critics to order candidates and a separately parameterized evaluator critic to review the selected value, then caps the reviewed value at the selector reference. Dynamic Adaptive Risk-aware Enhancement (DARE) then regulates each residual correction using candidate reliability, the gap between selector and evaluator signals, and a finite stage factor. Together, CARS, SEVA, and DARE form CARE-VI, an evidence-regulated target construction framework that preserves the backbone interfaces for critic regression and actor updates. The analysis bounds the CARS boundary error, the SEVA selected-value overestimation, and the one-sided deviation of the DARE residual displacement from its population counterpart, and establishes fixed-policy recovery after the finite-stage perturbation ends. Experiments with SAC, TD3, and TD7 on four MuJoCo tasks show that CARE-VI achieves the highest mean return in all twelve settings. Grouped ablations and scalar diagnostics support the roles of the three components in improving target reliability.

Xiang Zou, Shengzhu Shi, Junqi Gao +1

School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Temporal-Difference Learning Actor-Critic Methods Off-Policy RL

Aug 31, 2026cs.LG

Locally-Guided Actor-Critic: Training a Goal-conditioned Actor with a Subgoal-aware Critic

Goal-conditioned reinforcement learning struggles with long horizons when rewards are sparse. While a planner can provide subgoals to guide a low-level policy, its use at test time may introduce practical subgoal management difficulties. An alternative paradigm utilizes a high-level planner to assist learning, while the policy remains conditioned only on the final goal, enabling planner-free deployment. Among these methods, Reinforcement Learning with Imagined Subgoals (RIS) introduces a regularization term that encourages the policy to take the same actions for the final goal as it does for an intermediate goal. This regularization, however, may lead to goal-chaining issues when intermediate goals are low-dimensional. Potential-based reward shaping (PBRS) translates plans into an additional reward while ensuring that the optimal policy remains unchanged. Yet, it can generate deceptive rewards in terminal states. We study these failure cases and first propose an alternative reward shaping method (RS) that removes these deceptive rewards at the expense of theoretical guarantees of PBRS. Similar to this RS variant, we then propose another method named Locally-Guided Actor Critic (LG-AC) that rewards the agent for reaching intermediate goals. Unlike RS, where intermediate rewards are implicit in the shaping signal, we explicitly condition a value estimator on the full sequence of intermediate goals but represent the value function as a sum of subgoal-conditioned value functions, enabling dense hindsight relabeling. We evaluate all these methods in tasks with challenging goal-chaining requirements and empirically highlight specific cases in which either action regularization or reward shaping yield low performance, while LG-AC achieves the best overall performance across tasks.

Olivier Serris, Stéphane Doncieux, Olivier Sigaud

ISIR · Sorbonne Université, CNRS

Reinforcement Learning Sparse-Reward RL Actor-Critic Methods Reward Design for RL Goal-Conditioned RL

Aug 13, 2026cs.LG

The Time Value of Evolution

In evolutionary search, a weak child can be a valuable ancestor that makes high-fitness regions reachable. Immediate-return control is blind to this delayed utility, penalizing mutations through their immediate offspring even when they open productive future lineages. We formalize this hidden dynamic as the time value of evolution within a finite-horizon Markov decision process. To exploit it, we introduce Lineage-Value Policy Gradients (LVPG), a long-horizon actor-critic framework for automated trading policy discovery. Our architecture decouples search control into specialized policy heads over a shared generative backbone: a bootstrapped critic head estimates the value of finite-horizon lineage potential from multi-step mutation trees, while an actor head dynamically modulates mutation intensity over the remaining search budget. We isolate the impact of long-horizon credit assignment against immediate-return optimization across 90 paired runs under matched operators, lineage supervision, folds, seeds, and budgets. Path-based credit assignment substantially accelerates finite-budget search, increasing validation best-so-far AUC by 0.394 Sharpe units. LVPG also produces fewer temporary regressions than immediate-return optimization and recovers from them more often. Finite-horizon lineage value yields more selective non-monotonic search and stronger policies within identical resource constraints.

Matthew Siper, Ahmed Khalifa, Julian Togelius

Nof1, New York University · Nof1, University of Malta

Evolutionary Optimization Policy Gradient Methods Credit Assignment Actor-Critic Methods

Aug 7, 2026cs.LG

Learning Suffers More Than the Policy Class Under Partial Observability: A Closed-Form Analysis

When a reinforcement learning agent cannot observe the full state, we usually blame its policies: it cannot see enough to represent a good one. We show that in a solvable case the bigger problem lies elsewhere. Even when a good policy is available and the agent's value function is expressive enough to describe it exactly, learning still ends up somewhere far worse. We study a partially observed linear-quadratic problem in which a standard actor-critic learner can be solved in closed form. At our default setting the best policy the agent can represent is already close to optimal, costing 10.4% more than the ideal controller that observes everything. Learning does not find it. The algorithm instead comes to rest at a policy that is 35% worse than the best one available to it, and we can say exactly where and why. The cause is a bias in what the critic learns rather than a limit on what the actor can express. Because the agent cannot attribute what it sees to the part of the state it cannot observe, the critic misreads that unexplained variation as sharp curvature in its own value estimates, and the actor follows that error away from the optimum. We derive closed-form expressions for the resulting policy, for its cost, and for the one design choice that removes the problem, which is how far the learner looks ahead before trusting its own value estimates. Deep reinforcement learning experiments follow these predictions closely. Notably, giving the agent memory of past observations does not help, while changing how far it looks ahead does.

Idil Gözel

University College London · Department of Physics and Astronomy University College London, London, UK

RL Control Reinforcement Learning Partially Observable RL Temporal-Difference Learning Actor-Critic Methods Policy Learning

Aug 5, 2026eess.SY

Toward Integrating Adaptive Experience Replay and Online Uncertainty Estimation in Safe Actor-Critic Optimal Control

Safe actor-critic control often treats barrier filtering, uncertainty estimation, and experience replay as separate modules, even though each changes the data used for learning and control. We develop an integrated architecture in which the uncertainty estimate updates the obstacle geometry used by a control barrier function, filter interventions and estimation residuals determine replay priority, and the critic learns from the executed rather than nominal action. We instantiate the architecture on a two-dimensional robot-navigation task with corrupted obstacle measurements and compare six component-matched configurations under common training budgets, random seeds, sensor streams, exploration, and disturbances. Evaluation includes a moderate post-training test, an eleven-level perception-noise sweep, and an exploratory extreme-stress test at multiplier

6.0

. In the extreme test, the integrated configuration recorded no contacts and reached the goal in all five evaluation seeds. Its mean cost was

7.63\pm0.44

and its obstacle-belief root-mean-square error was

3.52\pm0.55

cm. The uncertainty-estimation ablation also recorded no contacts but reached the goal in four of five seeds, with mean cost

8.96\pm2.08

and belief error

11.08\pm1.23

cm. A finite-training bound clarifies replay exposure, and a robust barrier condition states the required estimation-error and feasibility assumptions. The results support coupling estimation, safety filtering, and replay on this benchmark; broader safety and convergence claims require further study.

Mahshad Rastegarmoghaddam, Davoud Nikkhouy, Shima Samadzadeh

Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy

RL Control Reinforcement Learning Robot Navigation Control Barrier Functions Safe RL Actor-Critic Methods

Aug 3, 2026cs.LG

Foundations of Reinforcement Learning and Control:Connections and New Perspectives

Reinforcement learning and control theory are two adjacent scientific fields that focus on optimizing the controller of unknown dynamical systems using feedback. While both fields have common roots in dynamic programming, they have evolved with distinct methodologies, goals, and cultures. Despite decades of mutual influence, a significant gap persists between the two communities. This tutorial introduces adaptive control, actor-critic reinforcement algorithms, and a new way to combine these two paradigms for data-driven decision making on a classical locomotion control problem. Our aim is to provide a foundation for understanding the core differences between the two approaches and insights to help experts in each field better understand and engage with the tools and approaches of the other.

Claire Vernade, Onno Eberhard, Martha White +4

University of Technology Nuremberg · Max Planck Institute for Intelligent Systems, Tübingen, Germany · University of Alberta and Alberta Machine Intelligence Institute (Amii) +2

RL Control Data-Driven Control Actor-Critic Methods Adaptive Control

Aug 2, 2026cs.LG

ReBRAC-v2: The Return of the King

Recent offline reinforcement learning methods increasingly rely on expressive generative policies and specialized value-guidance mechanisms. We ask whether comparable progress can instead come from systematically modernizing a conventional behavior-regularized actor-critic while preserving its algorithmic simplicity. We introduce ReBRAC-v2, which directly trains an exact-likelihood normalizing flow as the RL actor, combines likelihood, MSE, and MAE behavior regularization, and integrates a classification-based residual critic, staged optimization, and multi-sample test-time action selection. Rather than tuning this recipe separately for every task, we develop a single shared configuration via roughly 600 Bayesian proposals on six challenging OGBench tasks, freeze all structural and optimization choices, and adapt only two behavior-regularization coefficients over a 16-point grid. Across ten common state-based OGBench categories, ReBRAC-v2 averages 74.8 compared to 52.3 for the next-best aggregate result and ranks first in eight categories. The same recipe, without structural changes, obtains the strongest averages in our comparisons on D4RL AntMaze (90.2) and Adroit (33.6). Fixed-recipe ablations show the largest sensitivity to the selected mixed cloning objective, staged training, sufficient flow capacity, and multi-sample inference, while showing that several smaller choices depend on the values of other hyperparameters. These results show that disciplined, transferable engineering can achieve state-of-the-art aggregate performance without abandoning a minimalist offline RL foundation.

Denis Tarasov, Robert K. Katzschmann

Soft Robotics Lab, D-MAVT ETH Zurich, Switzerland

Reinforcement Learning Offline RL Actor-Critic Methods Policy Learning

Jul 30, 2026cs.LG

Hierarchical Multilevel Monte Carlo for Order-Optimal Neural Actor-Critic in Average-Reward CMDPs

Constrained Markov Decision Processes (CMDPs) provide a natural framework for reinforcement learning in safety-critical applications, where agents maximize long-term reward while satisfying long-term constraints. Although primal-dual actor-critic methods with linear critics are well understood, extending order-optimal convergence guarantees to neural critics in average-reward CMDPs has remained open. The main challenge is a fundamental bias-cost trade-off in neural critic estimation: under Neural Tangent Kernel (NTK) analysis, reducing critic bias substantially increases critic optimization cost, preventing order-optimal convergence in the primal-dual framework. We resolve this bottleneck by introducing a hierarchical Multilevel Monte Carlo (MLMC) neural critic that performs debiasing simultaneously across trajectory sampling and critic optimization. The resulting estimator attains the bias of a long critic optimization run with only logarithmic expected sample cost. Building on this estimator, we develop a primal-dual Natural Actor-Critic algorithm that achieves both an optimality gap and a constraint violation of order

\tilde{O}(T^{-1/2})

. This establishes the first order-optimal convergence guarantees for infinite-horizon average-reward CMDPs with general policy parameterization and neural critics, while eliminating the need to know the underlying mixing time. Our results are novel even in the unconstrained setting.

Ankur Naskar, Vaneet Aggarwal

Indian Institute of Science, India · Purdue University, USA

Average-Reward RL Constrained RL Actor-Critic Methods Policy Learning Variance Reduction

Jul 29, 2026cs.LG

Collaborative Weighting with Pessimistic Critic for Mitigating Overestimation in Off-Policy Reinforcement Learning

Deep off-policy reinforcement learning algorithms for continuous control typically rely on neural value function approximation to guide policy improvement. However, temporal-difference (TD) learning introduces noisy targets, resulting in non-stationary optimization, while greedy policy updates amplify early-stage estimation errors. The recursive propagation of such errors leads to persistent overestimation bias and degraded training stability in actor-critic methods. Existing approaches attempt to alleviate this issue via prioritized sampling or modified value learning objectives, but often overemphasize high-uncertainty transitions caused by limited data coverage or bootstrapping errors, thereby further amplifying bias.In this paper, we propose Collaborative Weighting Actor-Critic (CWAC), a unified framework that explicitly accounts for predictive uncertainty in value estimation. CWAC employs distributional critic to model return uncertainty and introduces a collaborative weighting mechanism that jointly reweights TD-errors and uncertainty, enabling robust learning from reliable samples while suppressing noisy updates. In addition, we incorporate a stochastic pessimistic value estimation scheme via sampling from the return distribution, which effectively mitigates error propagation during policy improvement. CWAC can be seamlessly integrated into existing off-policy algorithm frameworks such as SAC, TD3, and DDPG with minimal overhead. Empirical results demonstrate that our proposed method significantly enhances performance across a diverse range of simulated tasks. Our code is publicly available at https://anonymous.4open.science/r/CWAC-348E.

Gong Gao, Xiao Lai, Ziqi Xie +3

School of Computer Science and Technology, Tongji University, 200092, Shanghai, China · Shanghai University of Engineering Science, 201620, Shanghai, China

Reinforcement Learning Actor-Critic Methods Off-Policy RL

Jul 26, 2026cs.AI

Hybrid Advantage Estimation with Unified Critic for VLM Agentic Reinforcement Learning

Large Vision-Language Models (VLMs) now act as agents in interactive environments, where success requires coherent reasoning and decision-making across turns. Although end-to-end training in agentic environments can improve such multi-turn decision-making abilities, current methods mainly rely on either token-wise optimization over concatenated token trajectories or turn-wise optimization with uniform within-turn credit. In this work, we establish theoretical formulations for the two levels of optimization and derive a hybrid advantage that serves both objectives. Furthermore, with an appropriate choice of discount factor and learning target, we prove that a unified critic model can estimate values for both turn-wise and token-wise. As such, we propose HyGAE, an actor-critic framework that jointly optimizes token- and turn-level objectives with the hybrid advantage and unified critic. We conduct extensive evaluations of HyGAE across five multi-turn decision-making environments, where it achieves an average success rate of 91% and a significant improvement of 10% over other methods. Furthermore, we provide an in-depth analysis showing that the exact analytic form of the hybrid advantage and return is crucial for optimization. Project Page: https://wx-zhang.github.io/hygae-web/.

Wenxuan Zhang, Yuhui Wang, Donggang Jia +5

KAUST

Agentic RL Actor-Critic Methods RL for VLMs

Jul 21, 2026cs.AI

Comparative Study of Multi-Agent Actor-Critic Algorithms in Parameterized Action Reinforcement Learning

Parameterized action reinforcement learning has shown strong performance in environments requiring both discrete action selection and continuous parameterization. Prior work established the effectiveness of single-agent actor-critic algorithms - Greedy Actor-Critic (GAC), Soft Actor-Critic (SAC), and Truncated Quantile Critics (TQC) - on benchmark parameterized action tasks, but their extension to multi-agent settings remains largely unexplored. This paper presents a comparative study of shared-experience multi-agent extensions of these algorithms: Multi-Agent Greedy Actor-Critic (MAGAC), Multi-Agent Soft Actor-Critic (MASAC), and Multi-Agent Truncated Quantile Critics (MATQC). Rather than following the centralized training, decentralized execution (CTDE) paradigm, the proposed framework uses multiple independent actor-critic agents that share a replay buffer while maintaining separate policy and value networks. We evaluate the algorithms on the Platform-v0 and Goal-v0 benchmarks against their single-agent counterparts, using three-, five-, and ten-agent configurations to assess scalability. Performance is measured by average evaluation return and training time across ten independent runs, with one-way ANOVA and Tukey HSD post-hoc tests used to assess statistical significance. Results show that the multi-agent framework consistently improves Greedy Actor-Critic performance, while MASAC and MATQC show comparatively modest gains over their single-agent versions. Increasing the number of agents beyond five yields limited additional performance while substantially raising computational cost, particularly for MAGAC. These results highlight a trade-off between learning performance and computational efficiency, offering insight into the scalability of shared-experience multi-agent actor-critic methods for parameterized action reinforcement learning.

Ubayd Ali Bapoo, Clement N Nyirenda

Department of Computer Science University of the Western Cape Cape Town, South Africa

Reinforcement Learning Soft Actor-Critic Actor-Critic Methods Multi-Agent Reinforcement Learning

Jul 14, 2026cs.LG

Deconstructing Actor-Critic: A Large-scale Empirical Study of Design Components for Practitioners

Reinforcement learning is increasingly being considered for controlling real-world systems, from fusion plasma and autonomous vehicles to drug discovery and drinking water treatment, where reliability is essential and tuning budgets are limited. Actor-critic algorithms share a set of design decisions, such as how the policy is updated, how it represents the distribution over actions, how its gradient is estimated, and how often it is updated relative to the value estimator. Using a control task derived from a real water treatment plant, we analyze over 33,000 experiments to determine how these components affect variability across runs and sensitivity to hyperparameters. Common defaults, such as Gaussian action distributions with pathwise gradient estimators, are among the least reliable configurations, whereas bounded distributions with adaptive update schedules remain robust across a wide range of settings. These findings offer empirical guidance to practitioners across scientific and engineering domains for understanding and making component-level decisions when adapting actor-critic methods to new real-world control settings.

Haseeb Shah, Lingwei Zhu, Adam White +1

Department of Computing Science, University of Alberta, Canada · Alberta Machine Intelligence Institute (amii), Canada · Great Bay University, China +1

RL Control Reinforcement Learning Actor-Critic Methods

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 1, 2026cs.LG

Gauging, Measuring, and Controlling Critic Complexity in Actor-Critic Reinforcement Learning

Actor-critic methods depend on learned critics, but critic quality is often evaluated only indirectly through return, temporal-difference error, or value loss. Critic complexity is introduced as an additional diagnostic and intervention dimension for actor-critic reinforcement learning. The analysis uses spectral effective-rank entropy, a rank-like summary of the singular-value distributions of critic weight matrices, to assess critic model complexity. Across TD3 and PPO experiments, critic complexity is tracked together with return and Monte Carlo value-estimation bias. The results show that critic complexity is measurable throughout training and is systematically associated with training behavior, while also making clear that the relationship is heterogeneous across algorithms, tasks, and hyperparameters. A direct complexity-control intervention is then evaluated by adding a spectral-entropy penalty to the critic loss. This intervention reliably changes the targeted spectral quantity, demonstrating that critic complexity can be controlled rather than only observed. Return effects are treated as task-dependent evidence rather than as a general performance claim, because overall complexity-control results vary.

Konstantin Garbers

Peking University

Reinforcement Learning Actor-Critic Methods

Jun 25, 2026cs.LG

Revisiting Action Factorization for Complex Action Spaces

Many real-world control problems involve hybrid discrete-continuous action spaces. For example, steering and signaling in autonomous driving, and aiming and firing in robotics or video-games. Despite real-world hybrid factorization and reinforcement learning framework support for complex action spaces (e.g., Gymnasium, PettingZoo, TorchRL, SeedRL, Mujoco, etc), the default environments within those frameworks often implement uniform action space configurations (LunarLander, Walker2D, Cheetah, SMAC, SUMO, Ant, Atari). Landmark hybrid-action benchmarks (RoboCup 2D HFO, SC2LE, Platform, CARLA, etc) are mostly heavyweight or archival implementations originating from papers which test one or a small number of competing factorization methods on one kind of control. This article provides a cross-sectional study of factorization methods [independent networks, shared encoder, VDN, QPLEX, Joint, Auto-Regressive] on each of three families of algorithms [PPO, SAC, DQN] across three action spaces [discretized, hybrid, continuous] over four lightweight environments [Platform, hybrid-LunarLander, Hybrid-Shoot, CoopPush]. Accounting for some invalid pairings such as joint-continuous, we are left with 220 configurations to analyze each method. We provide two new C++ parallel gymnasium and petting-zoo compliant environments [CoopPush, Hybrid-Shoot] to isolate particular challenges such as state-dependent inter-action dependence. Finally, we introduce VDN-PPO and PPO-MIX which use a branching critic to assign credit to multi-headed PPO. These variants out-perform all other tested PPO factorizations. Our results suggest that branching dueling architectures balance compute and performance most effectively, with Auto-Regressive actions reaching the highest performance overall and native continuous SAC outperforming discrete and hybrid algorithms, albiet both at increased computational cost.

Timothy Flavin, Sandip Sen

The University of Tulsa, Tulsa, Oklahoma, USA

Reinforcement Learning Actor-Critic Methods

Jun 25, 2026math.OC

Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data

This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic differential equation, while only discrete-time transition data are available. In the model-based formulation, policy evaluation is naturally described by a stationary Hamilton-Jacobi-Bellman equation on

\mathcal P_2(\mathbb R^d)

, but this equation involves the drift and diffusion coefficients of the controlled McKean-Vlasov dynamics, which are not identifiable when only discrete-time data are available. On the other hand, a direct reduction to a time-discrete Bellman equation avoids the non-identifiability issue but loses the differential equation structure. To bridge these two viewpoints, we introduce a Mean-Field-PhiBE (MF-PhiBE), which incorporates discrete-time transition information into a continuous-time PDE on the Wasserstein space. The MF-PhiBE replaces the unknown infinitesimal drift and covariance in the policy-evaluation equation by one-step estimators computed from data, while preserving the generator structure of the McKean-Vlasov HJB equation. We also derive a policy-gradient theorem for entropy-regularized randomized feedback policies, expressing the actor direction through an action-wise infinitesimal advantage and the score of the policy. Combining these two ingredients yields a model-free actor-critic method. We prove a first-order consistency estimate showing that the value induced by an optimal MF-PhiBE policy approximates the optimal continuous-time value with an error of order

Δt

. In the linear-quadratic case, we show our approximation achieves second-order accuracy with only one-step data. Numerical experiments on an LQR benchmark and a crowd-aversion problem illustrate the proposed framework.

Erhan Bayraktar, Martin Hernandez, Qinxin Yan +1

Department of Mathematics, University of Michigan, Ann Arbor, MI, USA. · Department of Statistics and Data Science, University of California, Los Angeles, CA, USA. · Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA.

Reinforcement Learning Stochastic Optimal Control Continuous-Time RL Model-Free RL Actor-Critic Methods

Jun 24, 2026cs.LG

EVOM: Agentic Meta-Evolution of Actor-Critic Architectures for Reinforcement Learning

In actor-critic reinforcement learning, network architectures are typically manually designed. Automating this design is challenging because each candidate must be trained before evaluation, and the design space is open-ended. To address these challenges, we introduce EVOM, an agentic meta-evolution framework for discovering high-performance actor-critic architectures. We frame architecture search as a bi-level optimization: an inner loop trains weights via the low-fidelity proximal policy optimization (PPO), while an outer loop drives meta-evolution by iteratively refining architecture programs. Crucially, this outer loop is powered by an LLM-based design agent that operates purely as an architecture designer, completely decoupled from policy execution and environment control. Experiments reveal that EVOM outperforms the manually designed baseline, an LLM-guided random search, and the state-of-the-art LLM-guided programmatic policy search method MLES, delivering superior performance on Ant-v4 and HalfCheetah-v4. Ablation studies validate that both the meta-evolution loop and the LLM Design Agent are indispensable for final performance.

Boyun Zhang, Chao Wang, Kai Wu

Xidian University

Large Language Model-Guided NAS Neural Architecture Search Actor-Critic Methods Policy Learning

Jun 23, 2026cs.LG

Bias-Controlled Primal-Dual Natural Actor-Critic: Optimal Rates for Constrained Multi-Objective Average-Reward RL

Many reinforcement learning (RL) problems in the infinite-horizon average-reward setting require optimizing multiple conflicting objectives while satisfying multiple safety constraints. A common approach is concave scalarization, where the agent maximizes a utility

f(J^π_{r_1}, \ldots, J^π_{r_M})

subject to a scalarized constraint

g(J^π_{c_1}, \ldots, J^π_{c_N}) \ge 0

, where

J^π_{r_m}

and

J^π_{c_n}

denote the average-reward and cost under policy

π

. However, the nonlinearity of

f

and

g

introduces bias in policy-gradient and actor-critic methods, since gradients must be evaluated using noisy estimates of

J^π,

and

\mathbb{E}[\partial f(J^π)] \neq \partial f(\mathbb{E}[J^π]),

and this bias propagates through both primal and dual updates. We propose an MLMC-based primal-dual Natural Actor-Critic algorithm for average-reward MDPs that controls bias in scalarized objectives, constraint evaluation, and actor-critic estimation without requiring mixing-time knowledge. We show that the algorithm achieves optimal global convergence and constraint-violation rates of

\tilde{O}(1/\sqrt{T})

. To our knowledge, this is the first result establishing optimal convergence for concave scalarized multi-objective RL in the average-reward setting, both with and without constraints, and the first to do so without mixing-time information even in the absence of scalarization.

Ankur Naskar, Swetha Ganesh, Vaneet Aggarwal

Indian Institute of Science, Bengaluru, India · Purdue University, USA

Multi-Objective Reinforcement Learning Reinforcement Learning Average-Reward RL Constrained RL Actor-Critic Methods Policy Learning

Jun 10, 2026cs.RO

Critic Architecture Matters: Dual vs. Unified Critics for Humanoid Loco-Manipulation

Multi-objective reinforcement learning for humanoid robots must coordinate locomotion and manipulation within a single policy. A natural design choice is whether to use a single (unified) critic that estimates the combined value of all objectives, or separate (dual) critics with disjoint reward signals. We present a controlled comparison on the Unitree G1 humanoid (23 active DoF) in NVIDIA Isaac Lab, training loco-manipulation policies through a sequential curriculum spanning 13 levels from stationary reaching to walking with variable-orientation targets. In standardized evaluation, dual-critic policies reach targets 3.5

\times

faster (6.5 vs. 22.6 simulation steps), achieve 2

\times

higher throughput (14.3 vs. 7.0 validated reaches per 1,000 steps), and attain higher validated reach rates (65.2% vs. 53.8%) compared to the unified-critic policy. Notably, additional anti-gaming reward mechanisms provide no further improvement beyond the architectural change alone (60.9% vs. 65.2%). These results have direct implications for the emerging paradigm of RL fine-tuning of imitation-learned policies: when refining a pre-trained manipulation policy with RL, a unified critic risks suppressing the learned behavior through competing locomotion gradients. These findings demonstrate that critic architecture is a primary - and often overlooked - design choice in multi-objective humanoid RL, with greater impact than reward engineering on reaching efficiency.

Mehmet Turan Yardımcı

Department of Computer Engineering C¸ukurova University Adana, Türkiye

Multi-Objective Reinforcement Learning Humanoid Loco-Manipulation Humanoid Robot Control Actor-Critic Methods

Jun 9, 2026cs.MA

Phi-Actor-Critic: Steering General-Sum Games to Pareto-Efficient Correlated Equilibria

Real-world multi-agent systems, from traffic coordination to resource allocation, are often modeled as general-sum games where individual incentives conflict with collective welfare. In these settings, the central challenge is not merely finding an equilibrium, but selecting socially desirable outcomes among many suboptimal Nash equilibria. Standard deep multi-agent reinforcement learning (MARL) methods struggle with this problem, as value-decomposition approaches are constrained by monotonicity assumptions and policy-gradient methods often converge to stable but socially inefficient equilibria. To address this limitation, we propose

Φ

-Actor-Critic (

Φ

-AC), a framework that leverages swap regret minimization to steer learning toward high-welfare correlated equilibria (CE). To make counterfactual regret estimation tractable in deep MARL,

Φ

-AC employs a centralized attention critic that predicts vector-valued regrets in a single forward pass, avoiding computationally expensive counterfactual simulations. We further introduce a Lagrangian-based equilibrium selection mechanism that optimizes social welfare while enforcing stability through regret constraints. Experiments on matrix games, Multi-Agent Particle Environments (MPE), and the Melting Pot Harvest scenario demonstrate that

Φ

-AC learns efficient and stable coordination strategies across diverse mixed-motive settings while maintaining high collective return and competitive fairness.

Wongyu Lee, Francesco Lelli, Omran Ayoub +1

Politecnico di Milano · Tilburg University · University of Applied Sciences and Arts of Southern Switzerland

Multi-Agent Coordination Regret Minimization Actor-Critic Methods Cooperative MARL Multi-Agent Reinforcement Learning