Communication-Efficient Gradient Descent-Accent Methods for Distributed
  Variational Inequalities: Unified Analysis and Local Updates
Siqi Zhang Sayantan Choudhury Sebastian U Stich Nicolas Loizou
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.