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Twenty Questions with Noise: Bayes Optimal Policies for Entropy Loss
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 alsodoi:10.1017/s0021900200008895 fatcat:tabqiieeorcv3oa3dbu4cbiv3a