Stochastic Graph Neural Networks

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. However, current GNN implementations assume ideal distributed scenarios and ignore link fluctuations that occur due to environment or human factors. In these situations, the GNN fails to address its distributed task if the topological randomness is not considered accordingly. To overcome this issue, we put forth the stochastic graph neural network (SGNN) model: a GNN where the distributed graph convolutional operator is modified to account for the network changes. Since stochasticity brings in a new paradigm, we develop a novel learning process for the SGNN and introduce the stochastic gradient descent (SGD) algorithm to estimate the parameters. We prove through the SGD that the SGNN learning process converges to a stationary point under mild Lipschitz assumptions. Numerical simulations corroborate the proposed theory and show an improved performance of the SGNN compared with the conventional GNN when operating over random time varying graphs.