Federated learning (FL) for 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.

翻译：联邦学习中的极小极大优化为在分布式节点/客户端间训练模型提供了强大范式，既保护了数据隐私又增强了模型对数据异质性的鲁棒性。本文提出一种新型分布式极小极大优化算法\texttt{K-GT-Minimax}，该算法融合局部更新与梯度跟踪技术，深入探究了联邦极小极大优化的分布式实现。理论分析表明，该算法在处理非凸强凹极小极大优化问题时具有通信高效性与收敛速率，其收敛速度显著优于现有方法。\texttt{K-GT-Minimax}应对数据异质性与确保鲁棒性的能力，凸显了其在推进联邦学习研究与实践中的重要意义。