Journal of Applied Probability

Twenty questions with noise: Bayes optimal policies for entropy loss

Bruno Jedynak, Peter I. Frazier, and Raphael Sznitman

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

J. Appl. Probab., Volume 49, Number 1 (2012), 114-136.

First available in Project Euclid: 8 March 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 90B40: Search theory 90C39: Dynamic programming [See also 49L20]

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


Jedynak, Bruno; Frazier, Peter I.; Sznitman, Raphael. Twenty questions with noise: Bayes optimal policies for entropy loss. J. Appl. Probab. 49 (2012), no. 1, 114--136. doi:10.1239/jap/1331216837.

Export citation