This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured by its worst-case performance. We formulate the dynamic simulation budget allocation decision problem as a stochastic control problem under a Bayesian framework. Following the approximate dynamic programming theory, we derive a one-step-ahead dynamic optimal budget allocation policy and prove that this policy achieves consistency and asymptotic optimality. Numerical experiments demonstrate that the proposed procedure can significantly improve performance.

翻译：本研究考虑带输入不确定性的排序与选择问题，目标是在固定模拟预算下最大化正确选出最优方案的后验概率，其中每个方案由其最坏情况性能衡量。我们将动态模拟预算分配决策问题构建为贝叶斯框架下的随机控制问题。基于近似动态规划理论，我们推导出一种一步前瞻动态最优预算分配策略，并证明该策略具有一致性和渐近最优性。数值实验表明，所提方法能够显著提升性能。