联合界去往何处？最优臂识别与强FWER控制
Where Does the Union Bound Go? Best-Arm Identification and Strong FWER Control
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中文总结 AI 辅助
本研究探讨固定置信度最优臂识别中联合界的困惑，明确最优臂识别的两种假设定向方式，解释多重性的不同呈现形式，以跨领域术语明确其等价性。
中文摘要 AI 辅助
在固定置信度的最优臂识别中，证明常对竞争臂使用联合界。从多重检验视角看这令人困惑：若最优臂唯一，仅一个“臂i为最优”形式的假设为真，为何需要K-1的Bonferroni型因子？答案是假设存在两种自然定向方式：其一，最优臂识别本质是含K-1个真实零假设的强族式错误率（FWER）问题；其二，恰好一个零假设为真，但成对实现可能通过K-1次比较错误拒绝该零假设，故多重性未消失，仅出现在不同位置。本笔记以两个领域术语明确这种等价性。
英文摘要
In fixed-confidence best-arm identification, proofs often use a union bound across the competing arms. From a multiple-testing point of view this can look puzzling: if the best arm is unique, only one hypothesis of the form ``arm $i$ is best'' can be true. Why then should there be a Bonferroni-type factor of $K-1$? The answer is that there are two natural ways to orient the hypotheses. In one orientation, best-arm identification is literally a strong familywise-error-rate (FWER) problem with $K-1$ true nulls. In the opposite orientation, exactly one null is true, but a pairwise implementation can falsely reject that one null through any of $K-1$ comparisons. Thus the multiplicity has not disappeared; it just pops up in different places. This note makes the equivalence explicit in the terminology of both communities.
发表机构
- University of Twente（特温特大学）
- Centrum Wiskunde & Informatica（数学与计算机科学中心）
机构由 AI 辅助整理，请以论文原文为准。
