  Vertical federated learning (VFL) is a distributed learning paradigm, where
computing clients collectively train a model based on the partial features of
the same set of samples they possess. Current research on VFL focuses on the
case when samples are independent, but it rarely addresses an emerging scenario
when samples are interrelated through a graph. For graph-structured data, graph
neural networks (GNNs) are competitive machine learning models, but a naive
implementation in the VFL setting causes a significant communication overhead.
Moreover, the analysis of the training is faced with a challenge caused by the
biased stochastic gradients. In this paper, we propose a model splitting method
that splits a backbone GNN across the clients and the server and a
communication-efficient algorithm, GLASU, to train such a model. GLASU adopts
lazy aggregation and stale updates to skip aggregation when evaluating the
model and skip feature exchanges during training, greatly reducing
communication. We offer a theoretical analysis and conduct extensive numerical
experiments on real-world datasets, showing that the proposed algorithm
effectively trains a GNN model, whose performance matches that of the backbone
GNN when trained in a centralized manner.
