Twenty Questions with Noise: Bayes Optimal Policies for Entropy Loss

@article{Jedynak2012TwentyQW,
  title={Twenty Questions with Noise: Bayes Optimal Policies for Entropy Loss},
  author={Bruno Jedynak and Peter I. Frazier and Raphael Sznitman},
  journal={J. Applied Probability},
  year={2012},
  volume={49},
  pages={114-136}
}
We consider the problem of 20 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… CONTINUE READING
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