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Kernel-Based Reinforcement Learning: A Finite-Time Analysis
Omar Darwiche Domingues · Pierre Menard · Matteo Pirotta · Emilie Kaufmann · Michal Valko

Wed Jul 21 06:45 AM -- 06:50 AM (PDT) @ None
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 applies to a wide range of tasks. We empirically validate our approach in continuous MDPs with sparse rewards.

Author Information

Omar Darwiche Domingues (Inria)
Pierre Menard (Inria)
Matteo Pirotta (Facebook AI Research)
Emilie Kaufmann (CNRS, Univ. Lille, Inria)
Michal Valko (DeepMind / Inria / ENS Paris-Saclay)

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