Minimum Guesswork with an Unreliable Oracle

Natan Ardimanov, Ofer Shayevitz, Itzhak Tamo

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

Abstract

We study a guessing game where Alice holds a discrete random variable X, and Bob is trying to sequentially guess its value. Before the game begins, Bob can obtain side-information about X by asking an oracle, Carole, any binary question of his choosing. Carole's answer is unreliable, and is incorrect with probability \epsilon. We show that Bob should always ask Carole whether the index of X is odd or even with respect to a descending order of probabilities - this question minimizes all the guessing moments for any value of \epsilon. This in particular settles a conjecture of Burin and Shayevitz. We further count the number of optimal questions, and discuss some extensions including asymmetric channels from Carole to Bob and to multiple-choice questions.

Original languageEnglish
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages986-990
Number of pages5
ISBN (Print)9781538647806
DOIs
StatePublished - 15 Aug 2018
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: 17 Jun 201822 Jun 2018

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2018-June
ISSN (Print)2157-8095

Conference

Conference2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/TerritoryUnited States
CityVail
Period17/06/1822/06/18

Funding

FundersFunder number
Horizon 2020 Framework Programme639573
European Research Council
Israel Science Foundation1367/14

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