Entropy bounds on Bayesian learning

Olivier Gossner; Tristan Tomala

doi:10.1016/j.jmateco.2007.04.006

Entropy bounds on Bayesian learning

Olivier Gossner
, Tristan Tomala

France and IZA
Université Paris Dauphine

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

An observer of a process (x_t) believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P (x_t | x₁, ..., x_{t - 1}) and Q (x_t | x₁, ..., x_{t - 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.

langue originale	Anglais
Pages (de - à)	24-32
Nombre de pages	9
journal	Journal of Mathematical Economics
Volume	44
Numéro de publication	1
Les DOIs	https://doi.org/10.1016/j.jmateco.2007.04.006
état	Publié - 1 janv. 2008
Modification externe	Oui

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10.1016/j.jmateco.2007.04.006

Contient cette citation

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abstract = "An observer of a process (xt) 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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KW - Entropy

KW - Repeated decision problem

KW - Value of information

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Entropy bounds on Bayesian learning

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