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

TL;DR

This paper establishes lower bounds and introduces near-optimal, robust algorithms for distributed saddle point problems, including a new federated method validated through experiments on GAN training.

Contribution

It provides fundamental lower bounds, develops a new federated algorithm, and demonstrates its effectiveness in distributed GAN training.

Findings

Lower bounds for distributed saddle point methods

Near-optimal algorithms matching these bounds

Effective federated algorithm validated on GANs

Abstract

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 centralized 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 centralized distributed saddle-point problems - Extra Step Local SGD. The 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.