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Adaptive Wireless Power Allocation with Graph Neural Networks

We consider the problem of power control in wireless networks, consisting of multiple transmitter-receiver pairs communicating with each other over a single shared wireless medium. To achieve both a high total rate and a level of fairness across users, we formulate a policy optimization problem with constraints on the minimum per-user rate across network configurations with an adaptive slack parameter. To apply unsupervised learning algorithms in the dual domain, we parameterize the power control policy, slack variable, and dual parameters using graph neural networks (GNNs), which leverage the network topology to create a scalable and network-invariant processing architecture. We use a primal- dual algorithm to learn the optimal GNN parameters and demonstrate via numerical simulations the resulting GNNs' success in achieving the right balance between sum- and 5th percentile rates throughout a range of network configurations.