We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses learning using f -DRO and spectral/ L-risk minimization.

Then we come to the third term.

However, there are still two unsolved problems.

However, there are still two unsolved problems.

Then we come to the third term.

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.