DeepAI
Log In Sign Up

Decentralized Local Stochastic Extra-Gradient for Variational Inequalities

06/15/2021
by   Aleksandr Beznosikov, et al.
0

We consider decentralized stochastic variational inequalities where the problem data is distributed across many participating devices (heterogeneous, or non-IID data setting). We propose a novel method - based on stochastic extra-gradient - where participating devices can communicate over arbitrary, possibly time-varying network topologies. This covers both the fully decentralized optimization setting and the centralized topologies commonly used in Federated Learning. Our method further supports multiple local updates on the workers for reducing the communication frequency between workers. We theoretically analyze the proposed scheme in the strongly monotone, monotone and non-monotone setting. As a special case, our method and analysis apply in particular to decentralized stochastic min-max problems which are being studied with increased interest in Deep Learning. For example, the training objective of Generative Adversarial Networks (GANs) are typically saddle point problems and the decentralized training of GANs has been reported to be extremely challenging. While SOTA techniques rely on either repeated gossip rounds or proximal updates, we alleviate both of these requirements. Experimental results for decentralized GAN demonstrate the effectiveness of our proposed algorithm.

READ FULL TEXT

page 7

page 9

10/28/2019

Decentralized Parallel Algorithm for Training Generative Adversarial Nets

Generative Adversarial Networks (GANs) are powerful class of generative ...
08/22/2019

On the convergence of single-call stochastic extra-gradient methods

Variational inequalities have recently attracted considerable interest i...
06/10/2021

A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems

Min-max saddle point games have recently been intensely studied, due to ...
10/24/2018

Solving Weakly-Convex-Weakly-Concave Saddle-Point Problems as Weakly-Monotone Variational Inequality

In this paper, we consider first-order algorithms for solving a class of...
06/14/2021

Decentralized Personalized Federated Min-Max Problems

Personalized Federated Learning has recently seen tremendous progress, a...
10/10/2022

On the Performance of Gradient Tracking with Local Updates

We study the decentralized optimization problem where a network of n age...
11/16/2021

Stochastic Extragradient: General Analysis and Improved Rates

The Stochastic Extragradient (SEG) method is one of the most popular alg...