Entropy Bounds on Bayesian Learning
Gossner, Olivier; Tomala, Tristan (2008), Entropy Bounds on Bayesian Learning, Journal of Mathematical Economics, 44, 1, p. 24-32. http://dx.doi.org/10.1016/j.jmateco.2007.04.006
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Economics
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Abstract (EN)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.
Subjects / KeywordsBayesian learning; Repeated decision problem; Value of information; Entropy
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