Improved Bayesian Regret Bounds for Thompson Sampling in Reinforcement Learning

Ahmadreza Moradipari; Mohammad Pedramfar; Modjtaba Shokrian Zini; Vaneet Aggarwal

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arXiv · 2310.20007

Improved Bayesian Regret Bounds for Thompson Sampling in Reinforcement Learning

Ahmadreza Moradipari·Mohammad Pedramfar·Modjtaba Shokrian Zini·Vaneet Aggarwal

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Abstract

In this paper, we prove the first Bayesian regret bounds for Thompson Sampling in reinforcement learning in a multitude of settings. We simplify the learning problem using a discrete set of surrogate environments, and present a refined analysis of the information ratio using posterior consistency. This leads to an upper bound of order $\widetilde{O}(H\sqrt{d_{l_1}T})$ in the time inhomogeneous reinforcement learning problem where $H$ is the episode length and $d_{l_1}$ is the Kolmogorov $l_1-$dimension of the space of environments. We then find concrete bounds of $d_{l_1}$ in a variety of settings, such as tabular, linear and finite mixtures, and discuss how how our results are either the first of their kind or improve the state-of-the-art.

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BibTeX RIS

Ahmadreza Moradipari, Mohammad Pedramfar, Modjtaba Shokrian Zini, Vaneet Aggarwal. 2023-10-30. Improved Bayesian Regret Bounds for Thompson Sampling in Reinforcement Learning. https://arxiv.org/abs/2310.20007

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