Title: Data-driven Optimal Transport Cost Selection for Distributionally Robust Optimizatio,
Abstract: Recently, (Blanchet, Kang, and Murhy 2016) showed that several machine
learning algorithms, such as square-root Lasso, Support Vector Machines, and
regularized logistic regression, among many others, can be represented exactly
as distributionally robust optimization (DRO) problems. The distributional
uncertainty is defined as a neighborhood centered at the empirical
distribution. We propose a methodology which learns such neighborhood in a
natural data-driven way. We show rigorously that our framework encompasses
adaptive regularization as a particular case. Moreover, we demonstrate
empirically that our proposed methodology is able to improve upon a wide range
of popular machine learning estimators.