Kernel-Based Reinforcement Learning: A Finite-Time Analysis

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 $\tilde{O}\left(H^3{K}^{\frac{2d}{2d+1}}\right)$, 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.

Update following the publication in ICML 2021, including fixed typos

References in corpus (5)

• Provably Efficient Reinforcement Learning with Linear Function Approximation
• Tighter Problem-Dependent Regret Bounds in Reinforcement Learning without Domain Knowledge using Value Function Bounds
• Online Regret Bounds for Undiscounted Continuous Reinforcement Learning
• Model-based Reinforcement Learning and the Eluder Dimension
• Learning to Control in Metric Space with Optimal Regret