  Construction of ambiguity set in robust optimization relies on the choice of
divergences between probability distributions. In distribution learning,
choosing appropriate probability distributions based on observed data is
critical for approximating the true distribution. To improve the performance of
machine learning models, there has recently been interest in designing
objective functions based on Lp-Wasserstein distance rather than the classical
Kullback-Leibler (KL) divergence. In this paper, we derive concentration and
asymptotic results using Bregman divergence. We propose a novel asymmetric
statistical divergence called Wasserstein-Bregman divergence as a
generalization of L2-Wasserstein distance. We discuss how these results can be
applied to the construction of ambiguity set in robust optimization.
