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Main Authors: Šiška, David, Zhang, Yufei
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2605.22622
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author Šiška, David
Zhang, Yufei
author_facet Šiška, David
Zhang, Yufei
contents Wasserstein Policy Optimization (WPO) is a recently proposed reinforcement learning algorithm that leverages Wasserstein gradient flows to optimize stochastic policies in continuous action spaces. Despite its empirical success, the theoretical convergence properties of WPO in environments with continuous state and action spaces have yet to be fully established. In this note, we argue that WPO within the framework of entropy-regularised Markov Decision Processes converges linearly. This is done by leveraging recent advances in mean-field analysis for convergence of gradient flows using log-Sobole inequalities. Assuming existence of sufficiently regular solution to the gradient flow equation we demonstrate monotonic energy dissipation along the flow and establish a local log-Sobolev inequality. Ultimately, these properties allow us to argue that the value function should converge linearly to the global optimum.
format Preprint
id arxiv_https___arxiv_org_abs_2605_22622
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A note on convergence of Wasserstein policy optimization
Šiška, David
Zhang, Yufei
Machine Learning
Optimization and Control
Wasserstein Policy Optimization (WPO) is a recently proposed reinforcement learning algorithm that leverages Wasserstein gradient flows to optimize stochastic policies in continuous action spaces. Despite its empirical success, the theoretical convergence properties of WPO in environments with continuous state and action spaces have yet to be fully established. In this note, we argue that WPO within the framework of entropy-regularised Markov Decision Processes converges linearly. This is done by leveraging recent advances in mean-field analysis for convergence of gradient flows using log-Sobole inequalities. Assuming existence of sufficiently regular solution to the gradient flow equation we demonstrate monotonic energy dissipation along the flow and establish a local log-Sobolev inequality. Ultimately, these properties allow us to argue that the value function should converge linearly to the global optimum.
title A note on convergence of Wasserstein policy optimization
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2605.22622