On the Convergence of Clustered Federated Learning

Knowledge sharing and model personalization are essential components to tackle the non-IID challenge in federated learning (FL). Most existing FL methods focus on two extremes: 1) to learn a shared model to serve all clients with non-IID data, and 2) to learn personalized models for each client, namely personalized FL. There is a trade-off solution, namely clustered FL or cluster-wise personalized FL, which aims to cluster similar clients into one cluster, and then learn a shared model for all clients within a cluster. This paper is to revisit the research of clustered FL by formulating them into a bi-level optimization framework that could unify existing methods. We propose a new theoretical analysis framework to prove the convergence by considering the clusterability among clients. In addition, we embody this framework in an algorithm, named Weighted Clustered Federated Learning (WeCFL). Empirical analysis verifies the theoretical results and demonstrates the effectiveness of the proposed WeCFL under the proposed cluster-wise non-IID settings.