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This paper focuses on the distributed optimization of stochastic saddle pointproblems. The first part of the paper is devoted to lower bounds for thecenralized and decentralized distributed methods for smooth (strongly)convex-(strongly) concave saddle-point problems as well as the near-optimalalgorithms by which these bounds are achieved. Next, we present a new federatedalgorithm for cenralized distributed saddle point problems - Extra Step LocalSGD. Theoretical analysis of the new method is carried out for stronglyconvex-strongly concave and non-convex-non-concave problems. In theexperimental part of the paper, we show the effectiveness of our method inpractice. In particular, we train GANs in a distributed manner.

Distributed Saddle-Point Problems: Lower Bounds, Near-Optimal and Robust Algorithms