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。

方差减少的极大 - 极小优化算法实现快速分布式鲁棒学习

Fast Distributionally Robust Learning with Variance Reduced Min-Max  Optimization

Distributionally Robust Supervised Learning (DRSL) is necessary for building
reliable machine learning systems. When machine learning is deployed in the
real world, its performance can be significantly degraded because test data may
follow a different distribution from training data. DRSL with f-divergences
explicitly considers the worst-case distribution shift by minimizing the
adversarially reweighted training loss. In this paper, we analyze this DRSL,
focusing on the classification scenario. Since the DRSL is explicitly
formulated for a distribution shift scenario, we naturally expect it to give a
robust classifier that can aggressively handle shifted distributions. However,
surprisingly, we prove that the DRSL just ends up giving a classifier that
exactly fits the given training distribution, which is too pessimistic. This
pessimism comes from two sources: the particular losses used in classification
and the fact that the variety of distributions to which the DRSL tries to be
robust is too wide. Motivated by our analysis, we propose simple DRSL that
overcomes this pessimism and empirically demonstrate its effectiveness.

本文介绍了分布鲁棒监督学习（DRSL）的概念和其与 f - 散度的关系，DRSL 可以最小化对抗重加权训练损失来明确考虑最坏情况的分布移位，并在分类情景下进行了分析。研究发现 DRSL 恰好可以匹配给定的训练分布，提出了简单的 DRSL 以克服这种悲观主义，并且经验性地证明了其有效性。