We consider the penalized distributionally robust optimization (DRO) problem
with a closed, convex uncertainty set, a setting that encompasses the $f$-DRO,
Wasserstein-DRO, and spectral/$L$-risk formulations used in practice. We
present Drago, a stochastic primal-dual algorithm that achieves a
state-of-the-art linear convergence rate on strongly convex-strongly concave
DRO problems. The method combines both randomized and cyclic components with
mini-batching, which effectively handles the unique asymmetric nature of the
primal and dual problems in DRO. We support our theoretical results with
numerical benchmarks in classification and regression.

考虑给定一个闭合凸不确定性集合的罚函数分布鲁棒优化 (DRO) 问题，该问题涵盖了 $f$-DRO、Wasserstein-DRO 以及在实践中使用的谱 /$L$-risk 形式，我们提出了 Drago，这是一种基于随机原始对偶算法，能在强凸 - 强凹 DRO 问题上实现最先进的线性收敛率。该方法结合了随机化和循环成分以及小批量处理，能有效处理 DRO 中原始问题和对偶问题的独特的非对称性质。我们通过分类和回归的数值基准来支持我们的理论结果。