Distributionally robust supervised learning (DRSL) is emerging as a key
paradigm for building reliable machine learning systems for real-world
applications -- reflecting the need for classifiers and predictive models that
are robust to the distribution shifts that arise from phenomena such as
selection bias or nonstationarity. Existing algorithms for solving Wasserstein
DRSL -- one of the most popular DRSL frameworks based around robustness to
perturbations in the Wasserstein distance -- have serious limitations that
limit their use in large-scale problems -- in particular they involve solving
complex subproblems and they fail to make use of stochastic gradients. We
revisit Wasserstein DRSL through the lens of min-max optimization and derive
scalable and efficiently implementable stochastic extra-gradient algorithms
which provably achieve faster convergence rates than existing approaches. We
demonstrate their effectiveness on synthetic and real data when compared to
existing DRSL approaches. Key to our results is the use of variance reduction
and random reshuffling to accelerate stochastic min-max optimization, the
analysis of which may be of independent interest.

本文提出了一种可扩展的、可实现的随机额外梯度算法，用于解决 Wasserstein DRSL 框架下的分类问题，该算法采用方差缩减和随机重排，可达到更快的收敛速率，并在合成和真实数据上证明了其有效性。