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.

该研究探讨了一种用于固定预算最佳臂识别的局部渐近最小极值策略，并提出自适应广义Neyman分配（AGNA）策略，证明其在小间隙情况下最佳臂误识概率的最坏情况上界与最坏情况下界对齐。该策略是Neyman分配的一般化，并针对Glynn＆Juneja（2004）和Shin等人（2018）提出的现有策略进行了改进。相比于Komiyama等人（2022）提出的极小极大速率最优策略，我们提出的策略通过将分布类限制为小间隙分布，获得了更紧密的上界，包括常数项，并为固定预算最佳臂识别中的渐近最优策略的存在性问题做出了贡献。

自适应广义Neyman分配：局部渐近极小极优最佳臂识别