We consider the problem of 20 questions with noisy answers, in which we seek to nd 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.
['Bruno Jedynak', 'Peter I. Frazier', 'Raphael Sznitman']
TWENTY QUESTIONS WITH NOISE: BAYES OPTIMAL POLICIES FOR ENTROPY LOSS