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

Economics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	24-32
Number of pages	9
Journal	Journal of Mathematical Economics
Volume	44
Issue number	1
DOIs	https://doi.org/10.1016/j.jmateco.2007.04.006
State	Published - Jan 1 2008

Keywords

Bayesian learning
Entropy
Repeated decision problem
Value of information

ASJC Scopus subject areas

Economics and Econometrics
Applied Mathematics

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10.1016/j.jmateco.2007.04.006

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AB - 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 - Repeated decision problem

KW - Value of information

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Entropy bounds on Bayesian learning

Abstract

Keywords

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