Prophet secretary: Surpassing the 1 − 1/e barrier

Yossi Azar, Ashish Chiplunkar, Haim Kaplan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In the Prophet Secretary problem, samples from a known set of probability distributions arrive one by one in a uniformly random order, and an algorithm must irrevocably pick one of the samples as soon as it arrives. The goal is to maximize the expected value of the sample picked relative to the expected maximum of the distributions. This is one of the most simple and fundamental problems in online decision making that models the process selling one item to a sequence of costumers. For a closely related problem called the Prophet Inequality where the order of the random variables is adversarial, it is known that one can achieve in expectation 1/2 of the expected maximum, and no better ratio is possible. For the Prophet Secretary problem, that is, when the variables arrive in a random order, Esfandiari et al. (2015) showed that one can actually get 1 − 1/e of the maximum. The 1 − 1/e bound was recently extended to more general settings by Ehsani et al. (2018). Given these results, one might be tempted to believe that 1 − 1/e is the correct bound. We show that this is not the case by providing an algorithm for the Prophet Secretary problem that beats the 1 − 1/e bound and achieves 1 − 1/e + 1/400 times the expected maximum. We also prove a hardness result on the performance of algorithms under a natural restriction which we call deterministic distribution-insensitivity.

Original languageEnglish
Title of host publicationACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Number of pages16
ISBN (Electronic)9781450358293
StatePublished - 11 Jun 2018
Event19th ACM Conference on Economics and Computation, EC 2018 - Ithaca, United States
Duration: 18 Jun 201822 Jun 2018

Publication series

NameACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation


Conference19th ACM Conference on Economics and Computation, EC 2018
Country/TerritoryUnited States


  • Competitive analysis
  • Optimal stopping
  • Posted price mechanisms


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