  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
