KL-Entropy-Regularized RL with a Generative Model is Minimax Optimal

• URL: http://arxiv.org/abs/2205.14211v1
• Date: Fri, 27 May 2022 19:39:24 GMT
• Title: KL-Entropy-Regularized RL with a Generative Model is Minimax Optimal
• Authors: Tadashi Kozuno, Wenhao Yang, Nino Vieillard, Toshinori Kitamura, Yunhao Tang, Jincheng Mei, Pierre M\'enard, Mohammad Gheshlaghi Azar, Michal Valko, R\'emi Munos, Olivier Pietquin, Matthieu Geist, Csaba Szepesv\'ari
• Abstract summary: We consider and analyze the sample complexity of model reinforcement learning with a generative variance-free model. Our analysis shows that it is nearly minimax-optimal for finding an $varepsilon$-optimal policy when $varepsilon$ is sufficiently small.
• Score: 70.15267479220691
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we consider and analyze the sample complexity of model-free reinforcement learning with a generative model. Particularly, we analyze mirror descent value iteration (MDVI) by Geist et al. (2019) and Vieillard et al. (2020a), which uses the Kullback-Leibler divergence and entropy regularization in its value and policy updates. Our analysis shows that it is nearly minimax-optimal for finding an $\varepsilon$-optimal policy when $\varepsilon$ is sufficiently small. This is the first theoretical result that demonstrates that a simple model-free algorithm without variance-reduction can be nearly minimax-optimal under the considered setting.

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