Identifying clients with similar objectives and learning a model-per-cluster is an intuitive and interpretable approach to personalization in federated learning. However, doing so with provable and optimal guarantees has remained an open challenge. We formalize this problem as a stochastic optimization problem, achieving optimal convergence rates for a large class of loss functions. We propose simple iterative algorithms which identify clusters of similar clients and train a personalized model-per-cluster, using local client gradients and flexible constraints on the clusters. The convergence rates of our algorithms asymptotically match those obtained if we knew the true underlying clustering of the clients and are provably robust in the Byzantine setting where some fraction of the clients are malicious.

翻译：识别目标相似的客户端并学习每个聚类的模型，是联邦学习中一种直观且可解释的个性化方法。然而，以可证明且最优的保证实现这一目标，仍是一个未解决的挑战。我们将该问题形式化为随机优化问题，针对一大类损失函数实现了最优收敛速率。我们提出了简单的迭代算法，利用本地客户端梯度和对聚类的灵活约束，识别相似客户端的聚类，并为每个聚类训练个性化模型。这些算法的收敛速率在渐近意义上等同于已知客户端真实底层聚类时的收敛速率，并且在部分客户端存在恶意行为的拜占庭环境下具有可证明的鲁棒性。