As a popular paradigm for juggling data privacy and collaborative training, federated learning (FL) is flourishing to distributively process the large scale of heterogeneous datasets on edged clients. Due to bandwidth limitations and security considerations, it ingeniously splits the original problem into multiple subproblems to be solved in parallel, which empowers primal dual solutions to great application values in FL. In this paper, we review the recent development of classical federated primal dual methods and point out a serious common defect of such methods in non-convex scenarios, which we say is a "dual drift" caused by dual hysteresis of those longstanding inactive clients under partial participation training. To further address this problem, we propose a novel Aligned Federated Primal Dual (A-FedPD) method, which constructs virtual dual updates to align global consensus and local dual variables for those protracted unparticipated local clients. Meanwhile, we provide a comprehensive analysis of the optimization and generalization efficiency for the A-FedPD method on smooth non-convex objectives, which confirms its high efficiency and practicality. Extensive experiments are conducted on several classical FL setups to validate the effectiveness of our proposed method.

本研究解决了传统联邦原始对偶方法在非凸场景中存在的"双重漂移"问题，该问题由部分参与训练下长期不活跃客户端的双重滞后引起。提出了一种新的对齐联邦原始对偶（A-FedPD）方法，通过构建虚拟双重更新，使全球共识与本地双重变量对齐，提高了优化与泛化效率，并通过广泛实验验证了该方法的有效性。

对齐双重漂移：全联邦原始对偶学习所需