Over-the-Air Federated Graph Learning

Message-passing graph neural network (MPGNN) shows tremendous promise in modeling complex networks by capturing the interaction among vertices via the messaging-passing mechanism. However, the dimension of MPGNN is tied to the size of vertices in the graph, which varies from graph to graph, resulting in dimension mismatch that hinders the utilization of graph data distributed at the network edge. To address this issue, we in this paper leverage the attention mechanism to project the graph representation of MPGNNs into a unified space and apply over-the-air computation (AirComp) to support federated graph learning (FGL) over wireless networks. By explicitly deriving the upper bound on the convergence of over-the-air FGL, we formulate a long-term transmission distortion minimization problem, which is further decomposed into a series of online optimization problems by using Lyapunov optimization. We further propose a deep reinforcement learning based algorithm to optimize the AirComp transceiver, where the analytical expression of transmit power is exploited in the action design to reduce the searching space and also enhance the training performance. Simulations demonstrate that, compared to the benchmarks, the proposed algorithm attains two orders of magnitude acceleration in the inference stage, while exhibiting enhanced robustness and improving learning performance.