Year: 2025
Type: preprint
Abstract: We characterize a joint CLT of the number of pulls and the sample mean reward of the arms in a stochastic two-armed bandit environment under UCB algorithms. Several implications of this result are in place: (1) a nonstandard CLT of the number of pulls hence pseudo-regret that smoothly interpolates between a standard form in the large arm gap regime and a slow-concentration form in the small arm gap regime, and (2) a heuristic derivation of the sample bias up to its leading order from the correlation between the number of pulls and sample means. Our analysis framework is based on a novel perturbation analysis, which is of broader interest on its own.
Source: arXiv (Cornell University)
Authors: Chen, Yilun, Lu, Jiaqi
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W6929601701
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