In federated learning (FL), a cluster of local clients are chaired under the coordination of the global server and cooperatively train one model with privacy protection. Due to the multiple local updates and the isolated non-iid dataset, clients are prone to overfit into their own optima, which extremely deviates from the global objective and significantly undermines the performance. Most previous works only focus on enhancing the consistency between the local and global objectives to alleviate this prejudicial client drifts from the perspective of the optimization view, whose performance would be prominently deteriorated on the high heterogeneity. In this work, we propose a novel and general algorithm {\ttfamily FedSMOO} by jointly considering the optimization and generalization targets to efficiently improve the performance in FL. Concretely, {\ttfamily FedSMOO} adopts a dynamic regularizer to guarantee the local optima towards the global objective, which is meanwhile revised by the global Sharpness Aware Minimization (SAM) optimizer to search for the consistent flat minima. Our theoretical analysis indicates that {\ttfamily FedSMOO} achieves fast $\mathcal{O}(1/T)$ convergence rate with low generalization bound. Extensive numerical studies are conducted on the real-world dataset to verify its peerless efficiency and excellent generality.

提出一种联邦学习算法FedSMOO，通过与全局目标的动态正则化和全局Sharpness Aware Minimization（SAM）优化器，以及综合考虑优化和泛化目标，有效提高联邦学习的性能和通用性。

联邦学习中动态正则化的锐度感知极小化：接近全局一致性和光滑地形