Knowledge sharing and model personalization are two key components in the conceptual framework of personalized federated learning (PFL). Existing PFL methods focus on proposing new model personalization mechanisms while simply implementing knowledge sharing by aggregating models from all clients, regardless of their relation graph. This paper aims to enhance the knowledge-sharing process in PFL by leveraging the graph-based structural information among clients. We propose a novel structured federated learning (SFL) framework to learn both the global and personalized models simultaneously using client-wise relation graphs and clients' private data. We cast SFL with graph into a novel optimization problem that can model the client-wise complex relations and graph-based structural topology by a unified framework. Moreover, in addition to using an existing relation graph, SFL could be expanded to learn the hidden relations among clients. Experiments on traffic and image benchmark datasets can demonstrate the effectiveness of the proposed method. All implementation codes are available on Github
