标题： 最小最大和贝叶斯最优最佳臂识别：治疗选择的自适应实验设计 显示英文标题

标题： Minimax and Bayes Optimal Best-arm Identification: Adaptive Experimental Design for Treatment Choice

摘要： 本研究探讨了用于治疗选择的自适应实验设计，也称为固定预算最优臂识别。 我们考虑了一个包含治疗分配阶段和治疗选择阶段的自适应过程，并为此设置设计了一个自适应实验，以高效地识别最佳治疗臂，即具有最高期望结果的臂。 在我们设计的实验中，治疗分配阶段包括两个阶段。 第一阶段是预演阶段，在此阶段，我们将每个治疗臂均匀分配相等的比例，以消除明显次优的臂并估计结果方差。 在第二阶段，我们根据第一阶段估计的方差按比例分配治疗臂。 治疗分配阶段之后，该过程进入治疗选择阶段，在此阶段，我们选择样本均值最高的治疗臂作为最佳治疗臂的估计。 我们证明，这种单一设计在简单遗憾方面同时是渐近最小最大和贝叶斯最优的，其上界与我们的下界精确常数相匹配。 因此，我们设计的实验实现了尖锐的效率极限，而无需为最小最大和贝叶斯目标分别调整参数。 显示英文摘要

摘要： This study investigates adaptive experimental design for treatment choice, also known as fixed-budget best-arm identification. We consider an adaptive procedure consisting of a treatment-allocation phase followed by a treatment-choice phase, and we design an adaptive experiment for this setup to efficiently identify the best treatment arm, defined as the one with the highest expected outcome. In our designed experiment, the treatment-allocation phase consists of two stages. The first stage is a pilot phase, where we allocate each treatment arm uniformly with equal proportions to eliminate clearly suboptimal arms and estimate outcome variances. In the second stage, we allocate treatment arms in proportion to the variances estimated in the first stage. After the treatment-allocation phase, the procedure enters the treatment-choice phase, where we choose the treatment arm with the highest sample mean as our estimate of the best treatment arm. We prove that this single design is simultaneously asymptotically minimax and Bayes optimal for the simple regret, with upper bounds that match our lower bounds up to exact constants. Therefore, our designed experiment achieves the sharp efficiency limits without requiring separate tuning for minimax and Bayesian objectives.