Asymptotically Optimal Sampling Policy for Selecting Top-m Alternatives

Abstract

We consider selecting the top-m alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem and develop a sequential sampling policy that maximizes a value function approximation one-step look ahead. To show the asymptotic optimality of the proposed procedure, the asymptotically optimal sampling ratios that optimize the large deviations rate of the probability of false selection for selecting the top-m alternatives have been rigorously defined. The proposed sampling policy is not only proved to be consistent but also achieve the asymptotically optimal sampling ratios. Numerical experiments demonstrate superiority of the proposed allocation procedure over existing ones. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72250065, 72293582, 72022001, and 71901003], and the National Science Foundation [Grant DMS-2053489], the major project of the National Natural Science Foundation of China [Grant 72293582], and the China Scholarship Council [Grant CSC202206010152]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0333 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0333 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .