Federated learning (FL) on heterogeneous data (non-IID data) has recently received great attention. Most existing methods focus on studying the convergence guarantees for the global objective. While these methods can guarantee the decrease of the global objective in each communication round, they fail to ensure risk decrease for each client. In this paper, to address the problem,we propose FedCOME, which introduces a consensus mechanism to enforce decreased risk for each client after each training round. In particular, we allow a slight adjustment to a client's gradient on the server side, which generates an acute angle between the corrected gradient and the original ones of other clients. We theoretically show that the consensus mechanism can guarantee the convergence of the global objective. To generalize the consensus mechanism to the partial participation FL scenario, we devise a novel client sampling strategy to select the most representative clients for the global data distribution. Training on these selected clients with the consensus mechanism could empirically lead to risk decrease for clients that are not selected. Finally, we conduct extensive experiments on four benchmark datasets to show the superiority of FedCOME against other state-of-the-art methods in terms of effectiveness, efficiency and fairness. For reproducibility, we make our source code publicly available at: \url{https://github.com/fedcome/fedcome}.

在本文中，我们提出了一种名为FedCOME的共识机制，通过在服务器端对客户端的梯度进行微调，保证了每轮训练后每个客户端的风险减少；我们还设计了一种新的客户端采样策略，将共识机制推广到部分参与的联邦学习场景，有效地减少了未被选中的客户端的风险。通过在四个基准数据集上进行广泛实验证明了FedCOME在效果、效率和公平性方面优于其他最先进的方法。

异质数据上的一致性机制联邦学习：收敛性的新视角