Kernel-Based Reinforcement Learning: A Finite-Time Analysis

• URL: http://arxiv.org/abs/2004.05599v3
• Date: Wed, 23 Mar 2022 18:36:06 GMT
• Title: Kernel-Based Reinforcement Learning: A Finite-Time Analysis
• Authors: Omar Darwiche Domingues, Pierre M\'enard, Matteo Pirotta, Emilie Kaufmann, Michal Valko
• Abstract summary: We introduce Kernel-UCBVI, a model-based optimistic algorithm that leverages the smoothness of the MDP and a non-parametric kernel estimator of the rewards. We empirically validate our approach in continuous MDPs with sparse rewards.
• Score: 53.47210316424326
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning problems whose state-action space is endowed with a metric. We introduce Kernel-UCBVI, a model-based optimistic algorithm that leverages the smoothness of the MDP and a non-parametric kernel estimator of the rewards and transitions to efficiently balance exploration and exploitation. For problems with $K$ episodes and horizon $H$, we provide a regret bound of $\widetilde{O}\left( H^3 K^{\frac{2d}{2d+1}}\right)$, where $d$ is the covering dimension of the joint state-action space. This is the first regret bound for kernel-based RL using smoothing kernels, which requires very weak assumptions on the MDP and has been previously applied to a wide range of tasks. We empirically validate our approach in continuous MDPs with sparse rewards.

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