Entropy bounds on Bayesian learning

Olivier Gossner and Tristan Tomala
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Olivier Gossner: PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, Northwestern University [Evanston]

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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.

Keywords: Bayesian learning; Repeated decision problem; Value of information; Entropy (search for similar items in EconPapers)
Date: 2008-01
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Citations: View citations in EconPapers (3)

Published in Journal of Mathematical Economics, 2008, 44 (1), pp.24-32. ⟨10.1016/j.jmateco.2007.04.006⟩

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Journal Article: Entropy bounds on Bayesian learning (2008)
Working Paper: Entropy bounds on Bayesian learning (2008)
Working Paper: Entropy bounds on Bayesian learning (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-00754314

DOI: 10.1016/j.jmateco.2007.04.006

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