Fast decentralized gradient tracking for federated learning with local updates: From mini to minimax optimization

Federated learning (FL) for mini and minimax optimization has emerged as a powerful paradigm for training models across distributed nodes/clients while preserving data privacy and model robustness on data heterogeneity. In this work, we delve into the decentralized implementation of federated minimax optimization by proposing \texttt{K-GT-Minimax}, a novel decentralized minimax optimization algorithm that combines local updates and gradient tracking techniques. Our analysis showcases the algorithm's communication efficiency and convergence rate for nonconvex-strongly-concave (NC-SC) minimax optimization, demonstrating a superior convergence rate compared to existing methods. \texttt{K-GT-Minimax}'s ability to handle data heterogeneity and ensure robustness underscores its significance in advancing federated learning research and applications.