Abstract
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.
Funder
NSF, Directorate for Mathematical and Physical Sciences
Air Force Office of Scientific Research
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering