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Distributed and federated learning algorithms and techniques associatedprimarily with minimization problems. However, with the increase of minimaxoptimization and variational inequality problems in machine learning, thenecessity of designing efficient distributed/federated learning approaches forthese problems is becoming more apparent. In this paper, we provide a unifiedconvergence analysis of communication-efficient local training methods fordistributed variational inequality problems (VIPs). Our approach is based on ageneral key assumption on the stochastic estimates that allows us to proposeand analyze several novel local training algorithms under a single frameworkfor solving a class of structured non-monotone VIPs. We present the first localgradient descent-accent algorithms with provable improved communicationcomplexity for solving distributed variational inequalities on heterogeneousdata. The general algorithmic framework recovers state-of-the-art algorithmsand their sharp convergence guarantees when the setting is specialized tominimization or minimax optimization problems. Finally, we demonstrate thestrong performance of the proposed algorithms compared to state-of-the-artmethods when solving federated minimax optimization problems.

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