Kernel $\epsilon$-Greedy for Contextual Bandits

• URL: http://arxiv.org/abs/2306.17329v1
• Date: Thu, 29 Jun 2023 22:48:34 GMT
• Title: Kernel $\epsilon$-Greedy for Contextual Bandits
• Authors: Sakshi Arya and Bharath K. Sriperumbudur
• Abstract summary: We consider a kernelized version of the $epsilon$-greedy strategy for contextual bandits. We propose an online weighted kernel ridge regression estimator for the reward functions.
• Score: 4.1347433277076036
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider a kernelized version of the $\epsilon$-greedy strategy for contextual bandits. More precisely, in a setting with finitely many arms, we consider that the mean reward functions lie in a reproducing kernel Hilbert space (RKHS). We propose an online weighted kernel ridge regression estimator for the reward functions. Under some conditions on the exploration probability sequence, $\{\epsilon_t\}_t$, and choice of the regularization parameter, $\{\lambda_t\}_t$, we show that the proposed estimator is consistent. We also show that for any choice of kernel and the corresponding RKHS, we achieve a sub-linear regret rate depending on the intrinsic dimensionality of the RKHS. Furthermore, we achieve the optimal regret rate of $\sqrt{T}$ under a margin condition for finite-dimensional RKHS.

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