  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.
