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Asymptotically Optimal Sampling Policy for Selecting Top- m Alternatives

Author

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  • Gongbo Zhang

    (Department of Management Science and Information Systems, Guanghua School of Management, Peking University, Beijing 100871, China)

  • Yijie Peng

    (Department of Management Science and Information Systems, Guanghua School of Management, Peking University, Beijing 100871, China)

  • Jianghua Zhang

    (School of Management, Shandong University, Jinan 250100, China)

  • Enlu Zhou

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

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.

Suggested Citation

  • Gongbo Zhang & Yijie Peng & Jianghua Zhang & Enlu Zhou, 2023. "Asymptotically Optimal Sampling Policy for Selecting Top- m Alternatives," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1261-1285, November.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:6:p:1261-1285
    DOI: 10.1287/ijoc.2021.0333
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    References listed on IDEAS

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