Clustered Federated Learning based on Nonconvex Pairwise Fusion

This study investigates clustered federated learning (FL), one of the formulations of FL with non-i.i.d. data, where the devices are partitioned into clusters and each cluster optimally fits its data with a localized model. We propose a novel clustered FL framework, which applies a nonconvex penalty to pairwise differences of parameters. This framework can automatically identify clusters without a priori knowledge of the number of clusters and the set of devices in each cluster. To implement the proposed framework, we develop a novel clustered FL method called FPFC. Advancing from the standard ADMM, our method is implemented in parallel, updates only a subset of devices at each communication round, and allows each participating device to perform a variable amount of work. This greatly reduces the communication cost while simultaneously preserving privacy, making it practical for FL. We also propose a new warmup strategy for hyperparameter tuning under FL settings and consider the asynchronous variant of FPFC (asyncFPFC). Theoretically, we provide convergence guarantees of FPFC for general nonconvex losses and establish the statistical convergence rate under a linear model with squared loss. Our extensive experiments demonstrate the advantages of FPFC over existing methods.