March 2012 Twenty questions with noise: Bayes optimal policies for entropy loss
Bruno Jedynak, Peter I. Frazier, Raphael Sznitman
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J. Appl. Probab. 49(1): 114-136 (March 2012). DOI: 10.1239/jap/1331216837


We consider the problem of twenty questions with noisy answers, in which we seek to find a target by repeatedly choosing a set, asking an oracle whether the target lies in this set, and obtaining an answer corrupted by noise. Starting with a prior distribution on the target's location, we seek to minimize the expected entropy of the posterior distribution. We formulate this problem as a dynamic program and show that any policy optimizing the one-step expected reduction in entropy is also optimal over the full horizon. Two such Bayes optimal policies are presented: one generalizes the probabilistic bisection policy due to Horstein and the other asks a deterministic set of questions. We study the structural properties of the latter, and illustrate its use in a computer vision application.


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Bruno Jedynak. Peter I. Frazier. Raphael Sznitman. "Twenty questions with noise: Bayes optimal policies for entropy loss." J. Appl. Probab. 49 (1) 114 - 136, March 2012.


Published: March 2012
First available in Project Euclid: 8 March 2012

zbMATH: 1318.62017
MathSciNet: MR2952885
Digital Object Identifier: 10.1239/jap/1331216837

Primary: 60J20
Secondary: 62C10 , 90B40 , 90C39

Keywords: Bayesian experimental design , bisection , dynamic programing , entropy loss , object detection , search , sequential experimental design , Twenty questions

Rights: Copyright © 2012 Applied Probability Trust


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Vol.49 • No. 1 • March 2012
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