Year: 2023
Type: preprint
Abstract: We consider the $ε$-greedy strategy for the multi-arm bandit with covariates (MABC) problem, where the mean reward functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). We propose to estimate the unknown mean reward functions using an online weighted kernel ridge regression estimator, and show the resultant estimator to be consistent under appropriate decay rates of the exploration probability sequence, $\{ε_t\}_t$, and regularization parameter, $\{λ_t\}_t$. Moreover, we 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.
Source: arXiv (Cornell University)
Authors: Arya, Sakshi, Sriperumbudur, Bharath K.
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4383046481