Ambiguity set and learning via Bregman and Wasserstein
This work addresses the challenge of improving machine learning model performance through better divergence choices in distribution learning and robust optimization, though it appears incremental as it builds on existing Wasserstein and Bregman divergence concepts.
The paper tackles the problem of constructing ambiguity sets in robust optimization by proposing a novel asymmetric statistical divergence, Wasserstein-Bregman divergence, as a generalization of L2-Wasserstein distance, and derives concentration and asymptotic results using Bregman divergence to apply these findings to robust optimization.
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.