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Journal Articles Journal of Mathematical Economics Year : 2008

Entropy bounds on Bayesian learning

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.

Dates and versions

halshs-00754314 , version 1 (20-11-2012)

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Olivier Gossner, Tristan Tomala. Entropy bounds on Bayesian learning. Journal of Mathematical Economics, 2008, 44 (1), pp.24-32. ⟨10.1016/j.jmateco.2007.04.006⟩. ⟨halshs-00754314⟩
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