Federated averaging (FedAvg) is the most fundamental algorithm in Federated learning (FL). Previous theoretical results assert that FedAvg convergence and generalization degenerate under heterogeneous clients. However, recent empirical results show that FedAvg can perform well in many real-world heterogeneous tasks. These results reveal an inconsistency between FL theory and practice that is not fully explained. In this paper, we show that common heterogeneity measures contribute to this inconsistency based on rigorous convergence analysis. Furthermore, we introduce a new measure \textit{client consensus dynamics} and prove that \textit{FedAvg can effectively handle client heterogeneity when an appropriate aggregation strategy is used}. Building on this theoretical insight, we present a simple and effective FedAvg variant termed FedAWARE. Extensive experiments on three datasets and two modern neural network architectures demonstrate that FedAWARE ensures faster convergence and better generalization in heterogeneous client settings. Moreover, our results show that FedAWARE can significantly enhance the generalization performance of advanced FL algorithms when used as a plug-in module.

翻译：联邦平均（FedAvg）是联邦学习（FL）中最基础的算法。先前的理论结果断言，在异构客户端条件下，FedAvg的收敛性与泛化能力会退化。然而，近期的实证结果表明，FedAvg在许多现实世界的异构任务中表现良好。这些结果揭示了联邦学习理论与实践之间尚未得到充分解释的不一致性。本文通过严格的收敛性分析表明，常见的异构性度量指标是导致这种不一致性的原因之一。此外，我们引入了一种新的度量指标——客户端共识动态，并证明当采用合适的聚合策略时，FedAvg能够有效处理客户端异构性。基于这一理论洞见，我们提出了一种简单而有效的FedAvg变体，称为FedAWARE。在三个数据集和两种现代神经网络架构上进行的大量实验表明，FedAWARE在异构客户端设置下能确保更快的收敛和更好的泛化能力。此外，我们的结果表明，当作为插件模块使用时，FedAWARE能显著提升先进联邦学习算法的泛化性能。