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1 results

  • Twenty Questions with Noise: Bayes Optimal Policies for Entropy Loss

  • Part of
  • Bruno Jedynak, Peter I. Frazier, Raphael Sznitman
  • Journal:
    Journal of Applied Probability / Volume 49 / Issue 1 / March 2012
    Published online by Cambridge University Press:
    04 February 2016, pp. 114-136
    Print publication:
    March 2012
    • Article
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  • 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.