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Minimax and Bayes Optimal Best-Arm Identification

Masahiro Kato

arXiv 30 Jun 2025 · Econometrics

arXiv:2506.24007 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This study investigates minimax and Bayes optimal strategies in fixed-budget best-arm identification. We consider an adaptive procedure consisting of a sampling phase followed by a recommendation phase, and we design an adaptive experiment within this framework to efficiently identify the best arm, defined as the one with the highest expected outcome. In our proposed strategy, the sampling phase consists of two stages. The first stage is a pilot phase, in which we allocate each arm uniformly in equal proportions to eliminate clearly suboptimal arms and estimate outcome variances. In the second stage, arms are allocated in proportion to the variances estimated during the first stage. After the sampling phase, the procedure enters the recommendation phase, where we select the arm with the highest sample mean as our estimate of the best arm. We prove that this single strategy is simultaneously asymptotically minimax and Bayes optimal for the simple regret, with upper bounds that coincide exactly with our lower bounds, including the constant terms.

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36
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Junpei Komiyama, Kaito Ariu, Masahiro Kato, and Chao Qin (2023) Rate-optimal bayesian simple regret in best arm identification self0.9507486%
2Aurélien Garivier and Emilie Kaufmann (2016) Optimal best arm identification with fixed confidence0.9285480%
3Jean-Yves Audibert, Sébastien Bubeck, and Remi Munos (2010) Best arm identification in multi-armed bandits0.8434375%
4Tze Leung Lai and Herbert Robbins (1985) Asymptotically efficient adaptive allocation rules0.8434375%
5Emilie Kaufmann, Olivier Cappé, and Aurélien Garivier (2016) On the complexity of best-arm identification in multi-armed bandit models0.7946550%
6Sébastien Bubeck, Rémi Munos, and Gilles Stoltz (2011) Pure exploration in finitely-armed and continuous-armed bandits0.7375260%
7Kaito Ariu, Masahiro Kato, Junpei Komiyama, Kenichiro McAlinn, and C… (2021) Policy choice and best arm identification: Asymptotic analysis of exploration sampling, 2021 self0.7374275%
8Chun-Hung Chen, Jianwu Lin, Enver Yücesan, and Stephen E. Chick (2000) Simulation budget allocation for further enhancing the efficiency of ordinal optimization0.7373367%
9Rémy Degenne (2023) On the existence of a complexity in fixed budget bandit identification0.6444250%
10Emilie Kaufmann (2020) Contributions to the Optimal Solution of Several Bandits Problems0.6444250%

Showing the top 10 of 36 scored citations.