改进排序选择的有限预算分配，提升小样本下正确选中的概率。
Series Expansion of Probability of Correct Selection for Improved Finite Budget Allocation in Ranking and Selection
- 基于巴哈杜尔-拉奥展开，精确逼近有限样本下的正确选择概率。
- 提出的FCBA策略在小样本下显著优于传统方法，提升选中准确率。
- 解决低置信度场景下概率非单调问题，适合资源受限的优化任务。
本文针对排序与选择问题中有限样本性能不足的挑战，提出了概率正确选择（PCS）的巴哈杜尔-拉奥型展开式。传统大偏差近似在渐近情形下表现良好，但在有限样本下精度不足。本方法在仿真预算受限时提升了PCS的逼近精度，更准确刻画最优采样比例及依赖预算的最优性条件。算法上，提出一种新颖的有限预算分配（FCBA）策略，通过序贯估计最优性条件并动态调整采样比例。数值实验显示，相较于已有方法，FCBA在简化案例中实现了更优的PCS表现。进一步分析表明，文献中报道的低置信度场景下PCS的非单调行为，源于对多重错误二元比较的忽略。本文提供修正后的展开式和定制化分配策略，有效缓解该非单调性问题。
原文摘要 · Abstract (English)
This paper addresses the challenge of improving finite sample performance in Ranking and Selection by developing a Bahadur-Rao type expansion for the Probability of Correct Selection (PCS). While traditional large deviations approximations captures PCS behavior in the asymptotic regime, they can lack precision in finite sample settings. Our approach enhances PCS approximation under limited simulation budgets, providing more accurate characterization of optimal sampling ratios and optimality conditions dependent of budgets. Algorithmically, we propose a novel finite budget allocation (FCBA) policy, which sequentially estimates the optimality conditions and accordingly balances the sampling ratios. We illustrate numerically on toy examples that our FCBA policy achieves superior PCS performance compared to tested traditional methods. As an extension, we note that the non-monotonic PCS behavior described in the literature for low-confidence scenarios can be attributed to the negligence of simultaneous incorrect binary comparisons in PCS approximations. We provide a refined expansion and a tailored allocation strategy to handle low-confidence scenarios, addressing the non-monotonicity issue.
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