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}.

翻译：联邦学习在异构数据（非独立同分布数据）上的应用近期受到广泛关注。现有方法大多聚焦于全局目标的收敛性保证。虽然这些方法能保证每轮通信中全局目标函数的下降，但无法确保每个客户端风险的降低。为解决此问题，本文提出FedCOME方法，引入共识机制强制每个训练轮次后各客户端风险降低。具体而言，我们允许在服务器端对客户端梯度进行微调，使修正后的梯度与其他客户端原始梯度形成锐角。理论上证明了该共识机制可保证全局目标的收敛性。为将共识机制推广至部分参与联邦学习场景，我们设计了一种新颖的客户端采样策略，选取最能代表全局数据分布的客户端。结合共识机制对这些选定客户端进行训练，可在经验上导致未被选客户端风险降低。最后，我们在四个基准数据集上进行大量实验，证明FedCOME在有效性、效率和公平性方面优于其他最先进方法。为便于复现，我们在 \url{https://github.com/fedcome/fedcome} 公开了源代码。