  Recently, (Blanchet, Kang, and Murhy 2016, and Blanchet, and Kang 2017)
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.
