Data-Driven Optimal Transport Cost Selection For Distributionally Robust Optimization

By Jose H. Blanchet, Yang Kang, Karthyek Murthy, Fan Zhang. 2017

47 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Certifying Some Distributional Robustness with Principled Adversarial Training (2017, background): “Previous approaches to distributional robustness have considered finite-dimensional parametrizations for P, such as constraint sets for moments, support, or directional deviations [17, 20, 27], as well as non-parametric distances for probability measures such as f -divergences [5, 6, 40, 44, 21, 47]”
Regularization via Mass Transportation (2017, methodology): “[14] develop a systematic methodology for selecting the ground metric.”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, methodology): “A method for learning the best Mahalanobis norm from the training data is described in [11].”
Towards Out-Of-Distribution Generalization: A Survey (2021, background): “[22] propose a data-driven way to select the transportation cost function.”
Lipschitz Networks and Distributional Robustness (2018, background): “…the uncertainty set is a transportation cost-or Wasserstein-ball containing µ (deﬁned formally in § 2), under certain technical conditions, (1) has the dual form (Blanchet et al., 2016, 2017; Gao and Kleywegt, 2016; Shaﬁeezadeh-Abadeh et al., 2017) risk ℓ ( f ; P ) = risk ℓ ( f ; µ ) + L ( f ) .”