Prior-dependent analysis of posterior sampling reinforcement learning with function approximation

• URL: http://arxiv.org/abs/2403.11175v1
• Date: Sun, 17 Mar 2024 11:23:51 GMT
• Title: Prior-dependent analysis of posterior sampling reinforcement learning with function approximation
• Authors: Yingru Li, Zhi-Quan Luo,
• Abstract summary: This work advances randomized exploration in reinforcement learning (RL) with function approximation modeled by linear mixture MDPs. We establish the first prior-dependent Bayesian regret bound for RL with function approximation; and refine the Bayesian regret analysis for posterior sampling reinforcement learning (PSRL) We present an upper bound of $mathcalO(dsqrtH3 T log T)$, where $d$ represents the dimensionality of the transition kernel, $H$ the planning horizon, and $T$ the total number of interactions.
• Score: 19.505117288012148
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work advances randomized exploration in reinforcement learning (RL) with function approximation modeled by linear mixture MDPs. We establish the first prior-dependent Bayesian regret bound for RL with function approximation; and refine the Bayesian regret analysis for posterior sampling reinforcement learning (PSRL), presenting an upper bound of ${\mathcal{O}}(d\sqrt{H^3 T \log T})$, where $d$ represents the dimensionality of the transition kernel, $H$ the planning horizon, and $T$ the total number of interactions. This signifies a methodological enhancement by optimizing the $\mathcal{O}(\sqrt{\log T})$ factor over the previous benchmark (Osband and Van Roy, 2014) specified to linear mixture MDPs. Our approach, leveraging a value-targeted model learning perspective, introduces a decoupling argument and a variance reduction technique, moving beyond traditional analyses reliant on confidence sets and concentration inequalities to formalize Bayesian regret bounds more effectively.

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