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

翻译：本文重点论述散装最优化散装散装的马鞍问题。 第一部分专门论述关于( 强烈) 交织( 强力) 交织( 强力) 交织( 强力) 交织( 强力) 马鞍问题以及实现这些界限的近最佳算法的分流方法的下限。 其次, 我们为分流的马鞍问题提出一种新的联动算法 - 超步骤本地 SGD。 对新方法的理论分析针对强烈交织( 强力凝结) 和非交织( 非交织) 的分流问题。 在论文的实验部分, 我们展示了我们方法的实际效果, 特别是我们以分布方式培训 GANs 。