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Twenty questions with noise: Bayes optimal policies for entropy loss. (English) Zbl 1318.62017

Summary: 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.

MSC:

62C10 Bayesian problems; characterization of Bayes procedures
62H30 Classification and discrimination; cluster analysis (statistical aspects)
90B40 Search theory
90C39 Dynamic programming
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