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arXiv · 2004.05599

Kernel-Based Reinforcement Learning: A Finite-Time Analysis

Omar Darwiche Domingues·Pierre Ménard·Matteo Pirotta·Emilie Kaufmann·Michal Valko
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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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Omar Darwiche Domingues, Pierre Ménard, Matteo Pirotta, Emilie Kaufmann, Michal Valko. 2020-04-12. Kernel-Based Reinforcement Learning: A Finite-Time Analysis. https://arxiv.org/abs/2004.05599

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