Effective Method with Compression for Distributed and Federated Cocoercive Variational Inequalities

TL;DR

This paper introduces a novel compression-based method for solving distributed cocoercive variational inequalities, improving communication efficiency and stability in large-scale machine learning applications.

Contribution

It develops a new approach applying compression techniques to distributed variational inequalities with comprehensive convergence analysis.

Findings

High convergence speed demonstrated in experiments

Effective reduction in communication costs

Practical applicability confirmed through empirical results

Abstract

Variational inequalities as an effective tool for solving applied problems, including machine learning tasks, have been attracting more and more attention from researchers in recent years. The use of variational inequalities covers a wide range of areas - from reinforcement learning and generative models to traditional applications in economics and game theory. At the same time, it is impossible to imagine the modern world of machine learning without distributed optimization approaches that can significantly speed up the training process on large amounts of data. However, faced with the high costs of communication between devices in a computing network, the scientific community is striving to develop approaches that make computations cheap and stable. In this paper, we investigate the compression technique of transmitted information and its application to the distributed variational inequalities problem. In particular, we present a method based on advanced techniques originally developed for minimization problems. For the new method, we provide an exhaustive theoretical convergence analysis for cocoersive strongly monotone variational inequalities. We conduct experiments that emphasize the high performance of the presented technique and confirm its practical applicability.