We formulate, analyze and solve the problem of best arm identification with fairness constraints on subpopulations (BAICS). Standard best arm identification problems aim at selecting an arm that has the largest expected reward where the expectation is taken over the entire population. The BAICS problem requires that an selected arm must be fair to all subpopulations (e.g., different ethnic groups, age groups, or customer types) by satisfying constraints that the expected reward conditional on every subpopulation needs to be larger than some thresholds. The BAICS problem aims at correctly identify, with high confidence, the arm with the largest expected reward from all arms that satisfy subpopulation constraints. We analyze the complexity of the BAICS problem by proving a best achievable lower bound on the sample complexity with closed-form representation. We then design an algorithm and prove that the algorithm's sample complexity matches with the lower bound in terms of order. A brief account of numerical experiments are conducted to illustrate the theoretical findings.

翻译：本文提出、分析并解决了面向子群体的公平约束下的最优臂识别问题（BAICS）。标准最优臂识别问题旨在从整个群体中选取期望奖励最大的臂，而BAICS问题要求所选臂必须对所有子群体（例如不同种族、年龄组或客户类型）公平，即每个子群体上的条件期望奖励需满足预设阈值约束。BAICS问题的目标是以高置信度从满足子群体约束的所有臂中正确识别期望奖励最大的臂。我们通过证明具有闭式表达式的最优样本复杂度下界分析了BAICS问题的复杂度，进而设计了一种算法并证明其样本复杂度与下界在数量级上匹配。最后通过数值实验简要验证了理论结果。