Communication-Efficient Gradient Descent-Accent Methods for Distributed Variational Inequalities: Unified Analysis and Local Updates

TL;DR

This paper introduces a unified framework for communication-efficient local training algorithms tailored for distributed variational inequality problems, significantly improving convergence guarantees and performance in federated minimax optimization.

Contribution

It proposes the first local gradient descent-accent algorithms with provable improved communication complexity for distributed variational inequalities, unifying analysis across minimization and minimax problems.

Findings

Algorithms demonstrate superior communication efficiency.

Provable convergence guarantees for heterogeneous data.

Strong empirical performance in federated minimax tasks.

Abstract

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this paper, we provide a unified convergence analysis of communication-efficient local training methods for distributed variational inequality problems (VIPs). Our approach is based on a general key assumption on the stochastic estimates that allows us to propose and analyze several novel local training algorithms under a single framework for solving a class of structured non-monotone VIPs. We present the first local gradient descent-accent algorithms with provable improved communication complexity for solving distributed variational inequalities on heterogeneous data. The general algorithmic framework recovers state-of-the-art algorithms and their sharp convergence guarantees when the setting is specialized to minimization or minimax optimization problems. Finally, we demonstrate the strong performance of the proposed algorithms compared to state-of-the-art methods when solving federated minimax optimization problems.