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Neyman allocation is minimax optimal for best arm identification with two arms

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  • Karun Adusumilli

Abstract

This note describes the optimal policy rule, according to the local asymptotic minimax regret criterion, for best arm identification when there are only two treatments. It is shown that the optimal sampling rule is the Neyman allocation, which allocates a constant fraction of units to each treatment in a manner that is proportional to the standard deviation of the treatment outcomes. When the variances are equal, the optimal ratio is one-half. This policy is independent of the data, so there is no adaptation to previous outcomes. At the end of the experiment, the policy maker adopts the treatment with higher average outcomes.

Suggested Citation

  • Karun Adusumilli, 2022. "Neyman allocation is minimax optimal for best arm identification with two arms," Papers 2204.05527, arXiv.org, revised Aug 2022.
    • Handle: RePEc:arx:papers:2204.05527
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    File URL: http://arxiv.org/pdf/2204.05527
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    References listed on IDEAS

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    1. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    2. Maximilian Kasy & Anja Sautmann, 2021. "Adaptive Treatment Assignment in Experiments for Policy Choice," Econometrica, Econometric Society, vol. 89(1), pages 113-132, January.
    3. Masahiro Kato & Kaito Ariu & Masaaki Imaizumi & Masahiro Nomura & Chao Qin, 2022. "Optimal Best Arm Identification in Two-Armed Bandits with a Fixed Budget under a Small Gap," Papers 2201.04469, arXiv.org, revised Dec 2022.
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    Cited by:

    1. Chao Qin & Daniel Russo, 2024. "Optimizing Adaptive Experiments: A Unified Approach to Regret Minimization and Best-Arm Identification," Papers 2402.10592, arXiv.org, revised Jul 2024.
    2. Masahiro Kato, 2023. "Locally Optimal Fixed-Budget Best Arm Identification in Two-Armed Gaussian Bandits with Unknown Variances," Papers 2312.12741, arXiv.org, revised Mar 2024.

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