Local AdaGrad-Type Algorithm for Stochastic Convex-Concave Optimization

TL;DR

This paper introduces LocalAdaSEG, a communication-efficient, adaptive stochastic extragradient algorithm for large-scale convex-concave minimax problems, demonstrating theoretical speed-up and practical effectiveness in training GANs and solving bilinear games.

Contribution

The paper develops a novel distributed stochastic extragradient method with adaptive learning rates, reducing communication costs and achieving near-linear speed-up in convex-concave minimax optimization.

Findings

Achieves nearly linear speed-up in variance reduction.

Reduces communication costs via periodic communication strategy.

Effective in training GANs and solving bilinear games.

Abstract

Large scale convex-concave minimax problems arise in numerous applications, including game theory, robust training, and training of generative adversarial networks. Despite their wide applicability, solving such problems efficiently and effectively is challenging in the presence of large amounts of data using existing stochastic minimax methods. We study a class of stochastic minimax methods and develop a communication-efficient distributed stochastic extragradient algorithm, LocalAdaSEG, with an adaptive learning rate suitable for solving convex-concave minimax problems in the Parameter-Server model. LocalAdaSEG has three main features: (i) a periodic communication strategy that reduces the communication cost between workers and the server; (ii) an adaptive learning rate that is computed locally and allows for tuning-free implementation; and (iii) theoretically, a nearly linear speed-up with respect to the dominant variance term, arising from the estimation of the stochastic gradient, is proven in both the smooth and nonsmooth convex-concave settings. LocalAdaSEG is used to solve a stochastic bilinear game, and train a generative adversarial network. We compare LocalAdaSEG against several existing optimizers for minimax problems and demonstrate its efficacy through several experiments in both homogeneous and heterogeneous settings.