Twenty Questions with Noise: Bayes Optimal Policies for Entropy Loss

Bruno Jedynak, Peter I. Frazier, Raphael Sznitman
2012 Journal of Applied Probability  
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
more » ... ropy 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.
doi:10.1017/s0021900200008895 fatcat:tabqiieeorcv3oa3dbu4cbiv3a