Federated Learning (FL) is a rising approach towards collaborative and privacy-preserving machine learning where large-scale medical datasets remain localized to each client. However, the issue of data heterogeneity among clients often compels local models to diverge, leading to suboptimal global models. To mitigate the impact of data heterogeneity on FL performance, we start with analyzing how FL training influence FL performance by decomposing the global loss into three terms: local loss, distribution shift loss and aggregation loss. Remarkably, our loss decomposition reveals that existing local training-based FL methods attempt to reduce the distribution shift loss, while the global aggregation-based FL methods propose better aggregation strategies to reduce the aggregation loss. Nevertheless, a comprehensive joint effort to minimize all three terms is currently limited in the literature, leading to subpar performance when dealing with data heterogeneity challenges. To fill this gap, we propose a novel FL method based on global loss decomposition, called FedLD, to jointly reduce these three loss terms. Our FedLD involves a margin control regularization in local training to reduce the distribution shift loss, and a principal gradient-based server aggregation strategy to reduce the aggregation loss. Notably, under different levels of data heterogeneity, our strategies achieve better and more robust performance on retinal and chest X-ray classification compared to other FL algorithms. Our code is available at \href{https://github.com/Zeng-Shuang/FedLD}{https://github.com/Zeng-Shuang/FedLD}.

本研究针对联邦学习中客户数据异质性问题，该问题导致局部模型之间的偏差，影响全局模型的效果。我们提出了一种新颖的联邦学习方法FedLD，通过全局损失分解来共同减少局部损失、分布偏移损失和聚合损失，从而在不同数据异质性水平下实现了更好的性能和更强的鲁棒性，尤其是在视网膜和胸部X光图像分类任务中。 

通过损失分解应对联邦学习中的数据异质性