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Entropy bounds on Bayesian learning

Author

Listed:
  • Tristan Tomala

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Olivier Gossner

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

An observer of a process View the MathML source believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P(xt|x1,...,xt−1) and Q(xt|x1,...,xt−1) for t=1,...,n by a function of the relative entropy between the marginals of P and Q on the n first realizations. We apply this bound to the cost of learning in sequential decision problems and to the merging of Q to P.

Suggested Citation

  • Tristan Tomala & Olivier Gossner, 2008. "Entropy bounds on Bayesian learning," Post-Print hal-00464554, HAL.
    • Handle: RePEc:hal:journl:hal-00464554
    DOI: 10.1016/j.jmateco.2007.04.006
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    References listed on IDEAS

    as
    1. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
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    3. Kalai, Ehud & Lehrer, Ehud & Smorodinsky, Rann, 1999. "Calibrated Forecasting and Merging," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 151-169, October.
    4. Lehrer, Ehud & Smorodinsky, Rann, 2000. "Relative entropy in sequential decision problems1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 425-439, May.
    5. Ehud Lehrer & Rann Smorodinsky, 1996. "Compatible Measures and Merging," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 697-706, August.
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    7. D. Blackwell & L. Dubins, 2010. "Merging of Opinions with Increasing Information," Levine's Working Paper Archive 565, David K. Levine.
    8. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
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    Cited by:

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    3. Benjamin Van Roy & Xiang Yan, 2010. "Manipulation Robustness of Collaborative Filtering," Management Science, INFORMS, vol. 56(11), pages 1911-1929, November.

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