Expected Value Minimization in Information Theoretic Multiple Priors Models

I. Csiszár, Thomas Breuer

Research output: Article

1 Citation (Scopus)


Minimization of the expectation EP(X) of a random variable X over a family Γ of plausible prior distributions P is addressed, when Γ is a level set of some convex integral functional. As typical cases, Γ may be an I-divergence ball or some other f-divergence ball or Bregman distance ball. Regarding localization of the infimum we show that whether or not the minimum of EP(X) subject to P∈ Γ is attained, the densities of the almost minimizing distributions cluster around an explicitly specified function that may have integral less than 1 if the minimum is not attained. If Γ is an f-divergence ball of radius k, the minimum is either attained for any choice of k, or it is/is not attained when k is less/larger than a critical value. A conjecture is formulated about extending this result beyond f-divergence balls.

Original languageEnglish
JournalIEEE Transactions on Information Theory
Publication statusAccepted/In press - ápr. 19 2018

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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