%0 Journal Article %T Entropy bounds on Bayesian learning %+ Paris-Jourdan Sciences Economiques (PJSE) %+ Paris School of Economics (PSE) %+ Northwestern University [Evanston] %+ CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) %A Gossner, Olivier %A Tomala, Tristan %< avec comité de lecture %@ 0304-4068 %J Journal of Mathematical Economics %I Elsevier %V 44 %N 1 %P 24-32 %8 2008-01 %D 2008 %R 10.1016/j.jmateco.2007.04.006 %K Bayesian learning %K Repeated decision problem %K Value of information %K Entropy %Z Humanities and Social Sciences/Economics and FinanceJournal articles %X 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. %G English %L halshs-00754314 %U https://pjse.hal.science/halshs-00754314 %~ SHS %~ UNIV-PARIS1 %~ ENS-PARIS %~ ENPC %~ PJSE %~ PSE %~ CNRS %~ UNIV-DAUPHINE %~ EHESS %~ INRA %~ AO-ECONOMIE %~ CEREMADE %~ PARISTECH %~ PSL %~ AGREENIUM %~ INRAE %~ PSE-POST-PRINT %~ ENS-PSL %~ UNIV-DAUPHINE-PSL