发表机构
Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究固定预算最佳臂识别问题，对比算法与静态预言机，证明对于任意\(K\geq3\)及特定奖励，任何算法至少在一个实例中的错误衰减率至多为静态预言机的\((1 + \frac{\log(K)}{8})^{-1}\)倍，回答了相关开放问题。
AI 中文摘要
在固定预算最佳臂识别（也称为排序与选择）中，算法有采样预算可分配到\(K\)个臂上。每个样本提供关于该臂均值的噪声反馈，目标是识别出均值最大的臂。一个常见性能基准是静态预言机：一种提前知道均值并选择固定采样比例以最大化错误识别概率指数衰减率的非自适应策略。已构建多种自适应算法使其采样比例收敛到静态预言机比例。但对于所有问题实例，是否有算法能均匀匹配静态预言机的错误衰减率仍未解决；本文给出否定答案。对于任意\(K\geq3\)以及从任何单参数自然指数族抽取的奖励，证明对于任何算法，至少存在一个实例，其错误衰减率至多为静态预言机的\((1 + \frac{\log(K)}{8})^{-1}\)倍。这也回答了Qin(2022)提出的开放问题，表明固定预算最佳臂识别不存在复杂度。
英文摘要
In fixed-budget best-arm identification, also known as ranking and selection, an algorithm has a sampling budget to distribute across $K$ arms. Each sample provides noisy feedback about that arm's mean, and the goal is to identify the arm with the largest mean. A common performance benchmark is the static oracle: a non-adaptive strategy that knows the means in advance and chooses fixed sampling proportions to maximize the exponential decay rate of the probability of incorrect identification. Several adaptive algorithms have been constructed such that their sampling proportions converge to the static oracle proportions. However, it has remained open whether any algorithm could match the static oracle's error decay rate uniformly across all problem instances. We answer this in the negative. For any $K\ge 3$ and for rewards drawn from any one-parameter natural exponential family, we show that for any algorithm, there is at least one instance where the error decay rate is at most $\left(1 + \frac{\log(K)}{8}\right)^{-1}$ times that of the static oracle. This also answers the open question posed by Qin (2022), showing that fixed-budget best-arm identification does not admit a complexity.
