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.

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.

In this paper, we study communication-efficient decentralized training of large-scale machine learning models over a network. We propose and analyze SQuARM-SGD, a decentralized training algorithm, employing momentum and compressed communication between nodes regulated by a locally computable triggering rule. In SQuARM-SGD, each node performs a fixed number of local SGD (stochastic gradient descent) steps using Nesterov's momentum and then sends sparisified and quantized updates to its neighbors only when there is a significant change in its model parameters since the last time communication occurred. We provide convergence guarantees of our algorithm for strongly-convex and non-convex smooth objectives. We believe that ours is the first theoretical analysis for compressed decentralized SGD with momentum updates. We show that SQuARM-SGD converges at rate $\mathcal{O}\left(\frac{1}{nT}\right)$ for strongly-convex objectives, while for non-convex objectives it converges at rate $\mathcal{O}\left(\frac{1}{\sqrt{nT}}\right)$, thus matching the convergence rate of \emph{vanilla} distributed SGD in both these settings. We corroborate our theoretical understanding with experiments and compare the performance of our algorithm with the state-of-the-art, showing that without sacrificing much on the accuracy, SQuARM-SGD converges at a similar rate while saving significantly in total communicated bits.