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Personalized federated learning, as a variant of federated learning, trainscustomized models for clients using their heterogeneously distributed data.However, it is still inconclusive about how to design personalized models withbetter representation of shared global knowledge and personalized pattern. Tobridge the gap, we in this paper explore personalized models with low-rank andsparse decomposition. Specifically, we employ proper regularization to extracta low-rank global knowledge representation (GKR), so as to distill globalknowledge into a compact representation. Subsequently, we employ a sparsecomponent over the obtained GKR to fuse the personalized pattern into theglobal knowledge. As a solution, we propose a two-stage proximal-basedalgorithm named \textbf{Fed}erated learning with mixed \textbf{S}parse and\textbf{L}ow-\textbf{R}ank representation (FedSLR) to efficiently search forthe mixed models. Theoretically, under proper assumptions, we show that the GKRtrained by FedSLR can at least sub-linearly converge to a stationary point ofthe regularized problem, and that the sparse component being fused can convergeto its stationary point under proper settings. Extensive experiments alsodemonstrate the superior empirical performance of FedSLR. Moreover, FedSLRreduces the number of parameters, and lowers the down-link communicationcomplexity, which are all desirable for federated learning algorithms. Sourcecode is available in \url{https://github.com/huangtiansheng/fedslr}.

Fusion of Global and Local Knowledge for Personalized Federated Learning