# Data-driven Optimal Cost Selection for Distributionally Robust Optimization

## TL;DR

This paper introduces a data-driven method for selecting optimal cost parameters in distributionally robust optimization, improving machine learning estimators by adaptively defining distributional neighborhoods.

## Contribution

It proposes a novel framework that learns the neighborhood size in DRO models from data, encompassing adaptive regularization and enhancing estimator performance.

## Key findings

- Empirically improves various machine learning estimators.
- Framework adapts neighborhood size based on data.
- Encompasses adaptive regularization as a special case.

## Abstract

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.