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Wasserstein distance-based distributionally robust optimization (DRO) hasreceived much attention lately due to its ability to provide a robustnessinterpretation of various learning models. Moreover, many of the DRO problemsthat arise in the learning context admits exact convex reformulations and hencecan be tackled by off-the-shelf solvers. Nevertheless, the use of such solversseverely limits the applicability of DRO in large-scale learning problems, asthey often rely on general purpose interior-point algorithms. On the otherhand, there are very few works that attempt to develop fast iterative methodsto solve these DRO problems, which typically possess complicated structures. Inthis paper, we take a first step towards resolving the above difficulty bydeveloping a first-order algorithmic framework for tackling a class ofWasserstein distance-based distributionally robust logistic regression (DRLR)problem. Specifically, we propose a novel linearized proximal ADMM to solve theDRLR problem, whose objective is convex but consists of a smooth term plus twonon-separable non-smooth terms. We prove that our method enjoys a sublinearconvergence rate. Furthermore, we conduct three different experiments to showits superb performance on both synthetic and real-world datasets. Inparticular, our method can achieve the same accuracy up to 800+ times fasterthan the standard off-the-shelf solver.

A First-Order Algorithmic Framework for Wasserstein Distributionally Robust Logistic Regression