  Data-driven Distributionally Robust Optimization (DD-DRO) via optimal
transport has been shown to encompass a wide range of popular machine learning
algorithms. The distributional uncertainty size is often shown to correspond to
the regularization parameter. The type of regularization (e.g. the norm used to
regularize) corresponds to the shape of the distributional uncertainty. We
propose a data-driven robust optimization methodology to inform the
transportation cost underlying the definition of the distributional
uncertainty. We show empirically that this additional layer of robustification,
which produces a method we called doubly robust data-driven distributionally
robust optimization (DD-R-DRO), allows to enhance the generalization properties
of regularized estimators while reducing testing error relative to
state-of-the-art classifiers in a wide range of data sets.
