A Unified Approach for Solving Sequential Selection Problems

Alexander Goldenshluger, Yaakov Malinovsky, Assaf Zeevi, A Unified Approach for Solving Sequential Selection Problems, Probability, 2019, https://arxiv.org/abs/1901.04183

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Subjects

sequential selection
optimal stopping
secretary problems
relative ranks
full information problems
no–information problems

Abstract

In this paper we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as well as random problem horizons. The proposed framework is based on a reduction of the original selection problem to one of optimal stopping for a sequence of judiciously constructed independent random variables. We demonstrate that our approach allows exact and efficient computation of optimal policies and various performance metrics thereof for a variety of sequential selection problems, several of which have not been solved to date.