Georgy Yu. Sofronov and Tatiana V. Polushina
optimal stopping rules, multiple best choice problem, secretary problem, noisy optimization
Best choice problems can be considered one of the most interesting problems of sequential decision analysis. Problems of this type can arise in a wide variety of fields, including psychological, economical, and ecological applications. In this study, we consider a generalization of the best choice problem when it is possible to make more than one choice. We use the Cross-Entropy method to determine the optimal stopping rules and the value of a game. We include results of numerical experiments illustrating the effectiveness of the approach. We obtain estimates of the thresholds in the optimal stopping rules and compare the accuracy of these estimates with those obtained via asymptotic approximation.
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