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We prove the stability and global convergence of a coupled actor-critic gradient flow for infinite-horizon and entropy-regularised Markov decision processes (MDPs) in continuous state and action space with linear function approximation…

Optimization and Control · Mathematics 2025-10-17 Denis Zorba , David Šiška , Lukasz Szpruch

Entropy regularized algorithms such as Soft Q-learning and Soft Actor-Critic, recently showed state-of-the-art performance on a number of challenging reinforcement learning (RL) tasks. The regularized formulation modifies the standard RL…

Machine Learning · Statistics 2019-10-15 Elena Smirnova , Elvis Dohmatob

We prove under commonly used assumptions the convergence of actor-critic reinforcement learning algorithms, which simultaneously learn a policy function, the actor, and a value function, the critic. Both functions can be deep neural…

Machine Learning · Computer Science 2020-12-03 Markus Holzleitner , Lukas Gruber , José Arjona-Medina , Johannes Brandstetter , Sepp Hochreiter

We analyze the global convergence of the single-timescale actor-critic (AC) algorithm for the infinite-horizon discounted Markov Decision Processes (MDPs) with finite state spaces. To this end, we introduce an elegant analytical framework…

Machine Learning · Computer Science 2025-06-05 Navdeep Kumar , Priyank Agrawal , Giorgia Ramponi , Kfir Yehuda Levy , Shie Mannor

We provide theoretical guarantees for convergence of discrete-time policy mirror descent with inexact advantage functions updated using temporal difference (TD) learning for entropy regularised MDPs in Polish state and action spaces. We…

Optimization and Control · Mathematics 2026-02-12 Denis Zorba , David Šiška , Lukasz Szpruch

We show that the simplest actor-critic method -- a linear softmax policy updated with TD through interaction with a linear MDP, but featuring no explicit regularization or exploration -- does not merely find an optimal policy, but moreover…

Machine Learning · Computer Science 2022-03-15 Yuzheng Hu , Ziwei Ji , Matus Telgarsky

We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to…

Machine Learning · Computer Science 2017-05-23 Gergely Neu , Anders Jonsson , Vicenç Gómez

Natural actor-critic (NAC) and its variants, equipped with the representation power of neural networks, have demonstrated impressive empirical success in solving Markov decision problems with large state spaces. In this paper, we present a…

Machine Learning · Computer Science 2022-06-03 Semih Cayci , Niao He , R. Srikant

Natural policy gradient (NPG) methods with entropy regularization achieve impressive empirical success in reinforcement learning problems with large state-action spaces. However, their convergence properties and the impact of entropy…

Machine Learning · Computer Science 2026-02-17 Semih Cayci , Niao He , R. Srikant

In this work, we consider policy-based methods for solving the reinforcement learning problem, and establish the sample complexity guarantees. A policy-based algorithm typically consists of an actor and a critic. We consider using various…

Machine Learning · Computer Science 2023-01-16 Zaiwei Chen , Siva Theja Maguluri

Deterministic policy gradient algorithms are foundational for actor-critic methods in controlling continuous systems, yet they often encounter inaccuracies due to their dependence on the derivative of the critic's value estimates with…

Machine Learning · Computer Science 2025-02-11 Baturay Saglam , Dionysis Kalogerias

We present an actor-critic framework for MDPs where the objective is the variance-adjusted expected return. Our critic uses linear function approximation, and we extend the concept of compatible features to the variance-adjusted setting. We…

Machine Learning · Statistics 2013-10-15 Aviv Tamar , Shie Mannor

Soft actor-critic is a successful successor over soft Q-learning. While lived under maximum entropy framework, their relationship is still unclear. In this paper, we prove that in the limit they converge to the same solution. This is…

Machine Learning · Computer Science 2023-05-30 Jianfei Ma

We study infinite-horizon Constrained Markov Decision Processes (CMDPs) with general policy parameterizations and multi-layer neural network critics. Existing theoretical analyses for constrained reinforcement learning largely rely on…

Machine Learning · Computer Science 2026-03-10 Anirudh Satheesh , Pankaj Kumar Barman , Washim Uddin Mondal , Vaneet Aggarwal

In this paper, we study the role of the critic in actor--critic for entropy-regularized, finite, discounted environments. We establish that, when the critic is exact, using the latter as a baseline is a variance-reduction method in a strong…

Machine Learning · Computer Science 2026-05-26 Safwan Labbi , Paul Mangold , Daniil Tiapkin , Eric Moulines

In this paper we investigate the convergence of the Policy Iteration Algorithm (PIA) for a class of general continuous-time entropy-regularized stochastic control problems. In particular, instead of employing sophisticated PDE estimates for…

Optimization and Control · Mathematics 2025-04-24 Jin Ma , Gaozhan Wang , Jianfeng Zhang

Regularization of control policies using entropy can be instrumental in adjusting predictability of real-world systems. Applications benefiting from such approaches range from, e.g., cybersecurity, which aims at maximal unpredictability, to…

Systems and Control · Electrical Eng. & Systems 2026-02-18 Menno van Zutphen , Giannis Delimpaltadakis , Maurice Heemels , Duarte Antunes

We present the first class of policy-gradient algorithms that work with both state-value and policy function-approximation, and are guaranteed to converge under off-policy training. Our solution targets problems in reinforcement learning…

Artificial Intelligence · Computer Science 2018-02-23 Hamid Reza Maei

Although actor-critic methods have been successful in practice, their theoretical analyses have several limitations. Specifically, existing theoretical work either sidesteps the exploration problem by making strong assumptions or analyzes…

Machine Learning · Computer Science 2026-04-02 Max Qiushi Lin , Reza Asad , Kevin Tan , Haque Ishfaq , Csaba Szepesvari , Sharan Vaswani

On error of value function inevitably causes an overestimation phenomenon and has a negative impact on the convergence of the algorithms. To mitigate the negative effects of the approximation error, we propose Error Controlled Actor-critic…

Machine Learning · Computer Science 2021-09-08 Xingen Gao , Fei Chao , Changle Zhou , Zhen Ge , Chih-Min Lin , Longzhi Yang , Xiang Chang , Changjing Shang
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