Improved Algorithm for Adversarial Linear Mixture MDPs with Bandit Feedback and Unknown Transition

• URL: http://arxiv.org/abs/2403.04568v1
• Date: Thu, 7 Mar 2024 15:03:50 GMT
• Title: Improved Algorithm for Adversarial Linear Mixture MDPs with Bandit Feedback and Unknown Transition
• Authors: Long-Fei Li, Peng Zhao, Zhi-Hua Zhou
• Abstract summary: We study reinforcement learning with linear function approximation, unknown transition, and adversarial losses. We propose a new algorithm that attains an $widetildeO(dsqrtHS3K + sqrtHSAK)$ regret with high probability.
• Score: 71.33787410075577
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study reinforcement learning with linear function approximation, unknown transition, and adversarial losses in the bandit feedback setting. Specifically, we focus on linear mixture MDPs whose transition kernel is a linear mixture model. We propose a new algorithm that attains an $\widetilde{O}(d\sqrt{HS^3K} + \sqrt{HSAK})$ regret with high probability, where $d$ is the dimension of feature mappings, $S$ is the size of state space, $A$ is the size of action space, $H$ is the episode length and $K$ is the number of episodes. Our result strictly improves the previous best-known $\widetilde{O}(dS^2 \sqrt{K} + \sqrt{HSAK})$ result in Zhao et al. (2023a) since $H \leq S$ holds by the layered MDP structure. Our advancements are primarily attributed to (i) a new least square estimator for the transition parameter that leverages the visit information of all states, as opposed to only one state in prior work, and (ii) a new self-normalized concentration tailored specifically to handle non-independent noises, originally proposed in the dynamic assortment area and firstly applied in reinforcement learning to handle correlations between different states.

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