Data-driven Optimal Cost Selection for Distributionally Robust Optimization
Machine Learning
2020-02-25 v3
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.
Cite
@article{arxiv.1705.07152,
title = {Data-driven Optimal Cost Selection for Distributionally Robust Optimization},
author = {Jose Blanchet and Yang Kang and Fan Zhang and Karthyek Murthy},
journal= {arXiv preprint arXiv:1705.07152},
year = {2020}
}