Long-term Wireless Link Scheduling with State-Augmented Graph Neural Networks

We address the wireless link scheduling problem in large-scale wireless networks, subject to a minimum transmission requirement for each link. Unlike traditional approaches that aim to maximize instantaneous sum rate, we focus on maximizing long-term average performance, which better reflects the dynamic behavior of real-world networks. To this end, we formulate a constrained optimization problem that we solve by operating in the Lagrangian dual domain. The communication network is modeled as an undirected graph, from which we derive a conflict graph under a primary interference model, motivating the use of Graph Neural Networks (GNNs) to parameterize the scheduling policy. Since optimal scheduling decisions are inherently time-dependent when optimizing time averages, and GNNs are deterministic models, we incorporate state augmentation to handle the stochastic nature of the task. This augmentation enables the GNN to adapt scheduling decisions over time, balancing constraint satisfaction with performance maximization. We validate our approach through extensive numerical simulations, benchmarking against several baselines.