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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.
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Submitted on : Wednesday, March 17, 2010 - 2:20:50 PM
Last modification on : Thursday, February 7, 2019 - 4:20:17 PM

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Tristan Tomala, Olivier Gossner. Entropy bounds on Bayesian learning. Journal of Mathematical Economics, Elsevier, 2008, Vol.44,n°1, pp.24-32. ⟨10.1016/j.jmateco.2007.04.006⟩. ⟨hal-00464554⟩

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