Local Asymptotic Normality for Multi-Armed Bandits

Fuente: arXiv
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Main Authors: Akker, Ramon van den, Werker, Bas J. M., Zhou, Bo
Format: Preprint
Published: 2025
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author Akker, Ramon van den
Werker, Bas J. M.
Zhou, Bo
author_facet Akker, Ramon van den
Werker, Bas J. M.
Zhou, Bo
contents Van den Akker, Werker, and Zhou (2025) showed that the limit experiment, in the sense of H\a'{a}jek-Le Cam, for (contextual) bandits whose arms' expected payoffs differ by $O(T^{-1/2})$, is Locally Asymptotically Quadratic (LAQ) but highly non-standard, being characterized by a system of coupled stochastic differential equations. The present paper considers the complementary case where the arms' expected payoffs are fixed with a unique optimal (in the sense of highest expected payoff) arm. It is shown that, under sampling schemes satisfying mild regularity conditions (including UCB and Thompson sampling), the model satisfies the standard Locally Asymptotically Normal (LAN) property.
format Preprint
id arxiv_https___arxiv_org_abs_2512_12192
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Local Asymptotic Normality for Multi-Armed Bandits
Akker, Ramon van den
Werker, Bas J. M.
Zhou, Bo
Statistics Theory
Van den Akker, Werker, and Zhou (2025) showed that the limit experiment, in the sense of H\a'{a}jek-Le Cam, for (contextual) bandits whose arms' expected payoffs differ by $O(T^{-1/2})$, is Locally Asymptotically Quadratic (LAQ) but highly non-standard, being characterized by a system of coupled stochastic differential equations. The present paper considers the complementary case where the arms' expected payoffs are fixed with a unique optimal (in the sense of highest expected payoff) arm. It is shown that, under sampling schemes satisfying mild regularity conditions (including UCB and Thompson sampling), the model satisfies the standard Locally Asymptotically Normal (LAN) property.
title Local Asymptotic Normality for Multi-Armed Bandits
topic Statistics Theory
url https://arxiv.org/abs/2512.12192