J. Blanchet, Y. Kang, K. Murthy and F. Zhang, “Data-Driven Optimal Transport Cost Selection For Distributionally Robust Optimization,” 2019 Winter Simulation Conference (WSC), National Harbor, MD, USA, 2019, pp. 3740-3751, doi: 10.1109/WSC40007.2019.9004785. keywords: {Uncertainty;Measurement;Machine learning;Cost function;Perturbation methods;Robustness},

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Abstract

Some recent works 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 set is defined as a neighborhood centered at the empirical distribution, and the neighborhood is measured by optimal transport distance. In this paper, 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.

Authors
Jose Blanchet, Yang Kang, Karthyek Murthy, Fan Zhang
Publication date
2019/12/8
Conference
2019 winter simulation conference (WSC)
Pages
3740-3751
Publisher
IEEE