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 Probability Surveys > Vol. 17 (2020) open journal systems 


A unified approach for solving sequential selection problems

Alexander Goldenshluger, University of Haifa
Yaakov Malinovsky, University of Maryland
Assaf Zeevi, Columbia University


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.

AMS 2000 subject classifications: Primary 60G40; secondary 62L15

Keywords: Sequential selection, optimal stopping, secretary problems, relative ranks, full information problems, no–information problems.

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Goldenshluger, Alexander, Malinovsky, Yaakov, Zeevi, Assaf, A unified approach for solving sequential selection problems, Probability Surveys, 17, (2020), 214-256 (electronic). DOI: 10.1214/19-PS333.

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