To address the communication burden and privacy concerns associated with the centralized server in Federated Learning (FL), Decentralized Federated Learning (DFL) has emerged, which discards the server with a peer-to-peer (P2P) communication framework. However, most existing DFL algorithms are based on symmetric topologies, such as ring and grid topologies, which can easily lead to deadlocks and are susceptible to the impact of network link quality in practice. To address these issues, this paper proposes the DFedSGPSM algorithm, which is based on asymmetric topologies and utilizes the Push-Sum protocol to effectively solve consensus optimization problems. To further improve algorithm performance and alleviate local heterogeneous overfitting in Federated Learning (FL), our algorithm combines the Sharpness Aware Minimization (SAM) optimizer and local momentum. The SAM optimizer employs gradient perturbations to generate locally flat models and searches for models with uniformly low loss values, mitigating local heterogeneous overfitting. The local momentum accelerates the optimization process of the SAM optimizer. Theoretical analysis proves that DFedSGPSM achieves a convergence rate of $\mathcal{O}(\frac{1}{\sqrt{T}})$ in a non-convex smooth setting under mild assumptions. This analysis also reveals that better topological connectivity achieves tighter upper bounds. Empirically, extensive experiments are conducted on the MNIST, CIFAR10, and CIFAR100 datasets, demonstrating the superior performance of our algorithm compared to state-of-the-art optimizers.

基于不对称拓扑结构和Push-Sum协议，DFedSGPSM算法以解决共识优化问题为目标，结合Sharpness Aware Minimization（SAM）优化器和本地动量，提高算法性能并减轻联邦学习中的本地异质过拟合问题。理论分析证明在非凸平滑环境下，DFedSGPSM算法以O(1/√T)的收敛速率收敛于全局最优解，而更好的拓扑连接性能会得到更严格的上界。在MNIST、CIFAR10和CIFAR100数据集上进行的大量实验表明，与最先进的优化器相比，我们的算法具有更优越的性能。

非对称分散式联邦学习