  Learning on Graphs (LoG) is widely used in multi-client systems when each
client has insufficient local data, and multiple clients have to share their
raw data to learn a model of good quality. One scenario is to recommend items
to clients with limited historical data and sharing similar preferences with
other clients in a social network. On the other hand, due to the increasing
demands for the protection of clients' data privacy, Federated Learning (FL)
has been widely adopted: FL requires models to be trained in a multi-client
system and restricts sharing of raw data among clients. The underlying
potential data-sharing conflict between LoG and FL is under-explored and how to
benefit from both sides is a promising problem. In this work, we first
formulate the Graph Federated Learning (GFL) problem that unifies LoG and FL in
multi-client systems and then propose sharing hidden representation instead of
the raw data of neighbors to protect data privacy as a solution. To overcome
the biased gradient problem in GFL, we provide a gradient estimation method and
its convergence analysis under the non-convex objective. In experiments, we
evaluate our method in classification tasks on graphs. Our experiment shows a
good match between our theory and the practice.
