Kernelized Reinforcement Learning with Order Optimal Regret Bounds

• URL: http://arxiv.org/abs/2306.07745v3
• Date: Thu, 14 Mar 2024 13:36:01 GMT
• Title: Kernelized Reinforcement Learning with Order Optimal Regret Bounds
• Authors: Sattar Vakili, Julia Olkhovskaya,
• Abstract summary: $pi$KRVI is an optimistic modification of least trivial Hilbert-squares value. We prove the first order-optimal regret guarantees under a general setting. We show a sublinear regret bound that is order optimal in the case of Mat'ern kernels.
• Score: 11.024396385514864
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reinforcement learning (RL) has shown empirical success in various real world settings with complex models and large state-action spaces. The existing analytical results, however, typically focus on settings with a small number of state-actions or simple models such as linearly modeled state-action value functions. To derive RL policies that efficiently handle large state-action spaces with more general value functions, some recent works have considered nonlinear function approximation using kernel ridge regression. We propose $\pi$-KRVI, an optimistic modification of least-squares value iteration, when the state-action value function is represented by a reproducing kernel Hilbert space (RKHS). We prove the first order-optimal regret guarantees under a general setting. Our results show a significant polynomial in the number of episodes improvement over the state of the art. In particular, with highly non-smooth kernels (such as Neural Tangent kernel or some Mat\'ern kernels) the existing results lead to trivial (superlinear in the number of episodes) regret bounds. We show a sublinear regret bound that is order optimal in the case of Mat\'ern kernels where a lower bound on regret is known.

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