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 -