Bandit and covariate processes, with finite or non-denumerable set of arms

Tze Leung Lai, Michael Benjamin Sklar and Huanzhong Xu

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 1222-1237

Abstract: We introduce herein a new approach to nonparametric multi-armed bandit theory involving both the bandit and the covariate processes. Following Berry et al. (1997), we assume a non-denumerable set of arms for the bandit process. The approach we develop herein can be readily extended to continuous-time processes by using ε-greedy randomization and arm elimination instead of dynamic allocation indices. It also carries out a stochastic search with O(1) expected time for a nearly optimal arm at covariate values in a given set B before applying ε-greedy randomization and arm elimination. The procedure is shown to attain the asymptotically minimal rates for the regret over B.

Keywords: Multi-armed bandits; Infinite set of arms; Covariates for personalization; Adaptive allocation and its regret (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:150:y:2022:i:c:p:1222-1237

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DOI: 10.1016/j.spa.2022.03.010

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