Probability Surveys

A unified approach for solving sequential selection problems

Alexander Goldenshluger, Yaakov Malinovsky, and Assaf Zeevi

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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.

Article information

Probab. Surveys, Volume 17 (2020), 214-256.

Received: May 2019
First available in Project Euclid: 27 April 2020

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Digital Object Identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60]

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

Creative Commons Attribution 4.0 International License.


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

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