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.

翻译：我们考虑带闭凸不确定集的惩罚分布鲁棒优化(DRO)问题，该设定涵盖了实际应用中使用的$f$-DRO、Wasserstein-DRO和谱/$L$-风险形式。我们提出Drago算法——一种随机原始-对偶方法，在强凸-强凹DRO问题上实现了当前最优的线性收敛速率。该方法将随机分量与周期分量结合小批量处理，有效处理了DRO中原始问题和对偶问题独特的非对称性。我们通过分类与回归任务的数值基准实验支持了理论结果。