Volume 28, 2022
|Number of page(s)||38|
|Published online||27 January 2022|
Formulation and properties of a divergence used to compare probability measures without absolute continuity*,**
Division of Applied Mathematics, Brown University,
2 Quantitative Research, Susquehanna International Group, Bala Cynwyd, PA 19004, USA.
*** Corresponding author: firstname.lastname@example.org
Accepted: 6 January 2022
This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy. Also included are examples of computation and approximation of the divergence, and the demonstration of properties that are useful when one quantifies model uncertainty.
Mathematics Subject Classification: 60A10 / 62B10 / 93E15 / 94A17
Key words: Relative entropy / optimal transport theory / convex duality / calculus of variation / information-theoretic divergence / risk-sensitive control
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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