  Wasserstein distance-based distributionally robust optimization (DRO) has
received much attention lately due to its ability to provide a robustness
interpretation of various learning models. Moreover, many of the DRO problems
that arise in the learning context admits exact convex reformulations and hence
can be tackled by off-the-shelf solvers. Nevertheless, the use of such solvers
severely limits the applicability of DRO in large-scale learning problems, as
they often rely on general purpose interior-point algorithms. On the other
hand, there are very few works that attempt to develop fast iterative methods
to solve these DRO problems, which typically possess complicated structures. In
this paper, we take a first step towards resolving the above difficulty by
developing a first-order algorithmic framework for tackling a class of
Wasserstein distance-based distributionally robust logistic regression (DRLR)
problem. Specifically, we propose a novel linearized proximal ADMM to solve the
DRLR problem, whose objective is convex but consists of a smooth term plus two
non-separable non-smooth terms. We prove that our method enjoys a sublinear
convergence rate. Furthermore, we conduct three different experiments to show
its superb performance on both synthetic and real-world datasets. In
particular, our method can achieve the same accuracy up to 800+ times faster
than the standard off-the-shelf solver.
