揭示了最优臂识别与强族错误率控制的内在等价性
Where Does the Union Bound Go? Best-Arm Identification and Strong FWER Control
- 从多重检验视角重新理解最优臂识别的联合界应用
- 证明两种假设方向下均存在K-1重检验问题
- 适合关注统计推断与强化学习交叉的研究者
在固定置信度的最优臂识别中，证明常使用对竞争臂的联合界。从多重检验角度看这看似矛盾：若最优臂唯一，则仅一个形如“臂i为最优”的假设为真。为何仍需类似Bonferroni的K-1因子？答案在于假设方向的两种自然选择。一种方向下，最优臂识别本质上是具有K-1个真实零假设的强族错误率（FWER）问题；另一种方向下，仅一个零假设为真，但成对比较可能通过任意K-1种方式错误拒绝该假设。因此多重性并未消失，只是出现在不同位置。本文用两个领域的术语明确建立了这种等价性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。