Local SGD is a promising approach to overcome the communication overhead in distributed learning by reducing the synchronization frequency among worker nodes. Despite the recent theoretical advances of local SGD in empirical risk minimization, the efficiency of its counterpart in minimax optimization remains unexplored. Motivated by large scale minimax learning problems, such as adversarial robust learning and training generative adversarial networks (GANs), we propose local Stochastic Gradient Descent Ascent (local SGDA), where the primal and dual variables can be trained locally and averaged periodically to significantly reduce the number of communications. We show that local SGDA can provably optimize distributed minimax problems in both homogeneous and heterogeneous data with reduced number of communications and establish convergence rates under strongly-convex-strongly-concave and nonconvex-strongly-concave settings. In addition, we propose a novel variant local SGDA+, to solve nonconvex-nonconcave problems. We give corroborating empirical evidence on different distributed minimax problems.

本文提出了一种名为 local SGDA 的算法来缓解分布式学习中的通信开销，可在广泛的分布式 minmax 优化问题下实现可证明的收敛性和更少的通信次数。

局部随机梯度下降上升：收敛分析与通信效率