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Personalized Federated Learning (pFL) has gained attention for building a suite of models tailored to different clients. In pFL, the challenge lies in balancing the reliance on local datasets, which may lack representativeness, against the diversity of other clients’ models, whose quality and relevance are uncertain. Focusing on the clustered FL scenario, where devices are grouped based on similarities intheir data distributions without prior knowledge of cluster memberships, we develop a mathematical model for pFL using low-rank matrix optimization. Building on this formulation, we propose a pFL approach leveraging the Burer-Monteiro factorization technique. We examine the convergence guarantees of the proposed method, and present numerical experiments on training deep neural networks, demonstrating the empirical performance of the proposed method in scenarios where personalization is crucial. 

The key challenge of personalized federated learning (PerFL) is to capture the statistical heterogeneity properties of data with inexpensive communications and gain customized performance for participating devices. To address these, we introduced personalized federated learning in multi-tier architecture (PerMFL) to obtain optimized and personalized local models when there are known team structures across devices. We provide theoretical guarantees of PerMFL, which offers linear convergence rates for smooth strongly convex problems and sub-linear convergence rates for smooth non-convex problems. We conduct numerical experiments demonstrating the robust empirical performance of PerMFL, outperforming the state-of-the-art in multiple personalized federated learning tasks.

Federated learning (FL) has gained a lot of attention in recent years for building privacy-preserving collaborative learning systems. However, FL algorithms for constrained machine learning problems are still limited, particularly when the projection step is costly. To this end, we propose a Federated Frank-Wolfe Algorithm (FedFW). FedFW features data privacy, low per-iteration cost, and communication of sparse signals. In the deterministic setting, FedFW achieves an ε-suboptimal solution within O(ε^-2) iterations for smooth and convex objectives, and O(ε^-3) iterations for smooth but non-convex objectives. Furthermore, we present a stochastic variant of FedFW and show that it finds a solution within O(ε^-3) iterations in the convex setting. We demonstrate the empirical performance of FedFW on several machine learning tasks.