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

• URL: http://arxiv.org/abs/2405.19317v1
• Date: Wed, 29 May 2024 17:43:13 GMT
• Title: Adaptive Generalized Neyman Allocation: Local Asymptotic Minimax Optimal Best Arm Identification
• Authors: Masahiro Kato,
• Abstract summary: This study investigates a local minimax optimal strategy for fixed-budget best arm identification (BAI) We 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.
• Score: 10.470114319701576
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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