Twenty questions with noise: Bayes optimal policies for entropy loss
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.
Permanent link to this document: http://projecteuclid.org/euclid.jap/1331216837
Digital Object Identifier: doi:10.1239/jap/1331216837
Zentralblatt MATH identifier: 06026104
Mathematical Reviews number (MathSciNet): MR2952885