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Adaptive Generalized Neyman Allocation: Local Asymptotic Minimax Optimal Best Arm Identification

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  • Masahiro Kato

Abstract

This study investigates a local asymptotic minimax optimal strategy for fixed-budget best arm identification (BAI). We propose the Adaptive Generalized Neyman Allocation (AGNA) strategy and show that its worst-case upper bound of the probability of misidentifying the best arm aligns with the worst-case lower bound under the small-gap regime, where the gap between the expected outcomes of the best and suboptimal arms is small. Our strategy corresponds to a generalization of the Neyman allocation for two-armed bandits (Neyman, 1934; Kaufmann et al., 2016) and a refinement of existing strategies such as the ones proposed by Glynn & Juneja (2004) and Shin et al. (2018). Compared to Komiyama et al. (2022), which proposes a minimax rate-optimal strategy, our proposed strategy has a tighter upper bound that exactly matches the lower bound, including the constant terms, by restricting the class of distributions to the class of small-gap distributions. Our result contributes to the longstanding open issue about the existence of asymptotically optimal strategies in fixed-budget BAI, by presenting the local asymptotic minimax optimal strategy.

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  • Masahiro Kato, 2024. "Adaptive Generalized Neyman Allocation: Local Asymptotic Minimax Optimal Best Arm Identification," Papers 2405.19317, arXiv.org.
    • Handle: RePEc:arx:papers:2405.19317
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    References listed on IDEAS

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    1. Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2011. "Adaptive Experimental Design Using the Propensity Score," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 96-108, January.
    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. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    4. Kaito Ariu & Masahiro Kato & Junpei Komiyama & Kenichiro McAlinn & Chao Qin, 2021. "Policy Choice and Best Arm Identification: Asymptotic Analysis of Exploration Sampling," Papers 2109.08229, arXiv.org, revised Nov 2021.
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