PolieDRO: a novel classification and regression framework with non-parametric data-driven regularization

PolieDRO is a novel analytics framework for classification and regression that harnesses the power and flexibility of data-driven distributionally robust optimization (DRO) to circumvent the need for regularization hyperparameters. Recent literature shows that traditional machine learning methods such as SVM and (square-root) LASSO can be written as Wasserstein-based DRO problems. Inspired by those results we propose a hyperparameter-free ambiguity set that explores the polyhedral structure of data-driven convex hulls, generating computationally tractable regression and classification methods for any convex loss function. Numerical results based on 100 real-world databases and an extensive experiment with synthetically generated data show that our methods consistently outperform their traditional counterparts.