TY - GEN

T1 - Prophet secretary

T2 - 19th ACM Conference on Economics and Computation, EC 2018

AU - Azar, Yossi

AU - Chiplunkar, Ashish

AU - Kaplan, Haim

N1 - Publisher Copyright:
© 2018 Copyright held by the owner/author(s). Publication rights licensed to ACM.

PY - 2018/6/11

Y1 - 2018/6/11

N2 - 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.

AB - 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.

KW - Competitive analysis

KW - Optimal stopping

KW - Posted price mechanisms

UR - http://www.scopus.com/inward/record.url?scp=85050111211&partnerID=8YFLogxK

U2 - 10.1145/3219166.3219182

DO - 10.1145/3219166.3219182

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85050111211

T3 - ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation

SP - 303

EP - 318

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

PB - Association for Computing Machinery, Inc

Y2 - 18 June 2018 through 22 June 2018

ER -