Wasserstein distributionally robust optimization yields data-driven decisions that are computable as convex programs and have finite-sample out-of-sample guarantees, and this tutorial unifies the theory with machine learning applications.
Data-driven Optimal Cost Selection for Distributionally Robust Optimization
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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.
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Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning
Wasserstein distributionally robust optimization yields data-driven decisions that are computable as convex programs and have finite-sample out-of-sample guarantees, and this tutorial unifies the theory with machine learning applications.