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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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    Cited by:

    1. Ekmekci, Mehmet & Gossner, Olivier & Wilson, Andrea, 2012. "Impermanent types and permanent reputations," Journal of Economic Theory, Elsevier, vol. 147(1), pages 162-178.
    2. Benjamin Van Roy & Xiang Yan, 2009. "Manipulation Robustness of Collaborative Filtering Systems," Working Papers 09-21, NET Institute, revised Sep 2009.
    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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