# Doubly Robust Data-Driven Distributionally Robust Optimization

## TL;DR

This paper introduces a novel doubly robust data-driven distributionally robust optimization method that improves generalization and reduces testing error by adaptively informing the transportation cost in distributional uncertainty.

## Contribution

It proposes a new methodology to adaptively determine the transportation cost in DD-DRO, enhancing robustness and generalization over existing regularized estimators.

## Key findings

- Empirically improves generalization in various datasets.
- Reduces testing error compared to state-of-the-art classifiers.
- Enhances robustness by adaptively informing distributional uncertainty.

## Abstract

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.