Transferable Policies for Large Scale Wireless Networks with Graph Neural Networks

We consider the problem of finding optimal power allocations subject to system constraints in ad-hoc wireless networks. The resulting optimization problem has the form of a constrained learning problem, motivating the use of a function parameterization such as a neural network. While such a policy can be trained with a primal-dual learning method, traditional neural network architectures are unsuitable for execution in wireless networks, as such networks change frequently in practice, rendering the learned neural network ineffective. To learn a transferable policy that can generalize to varying and growing networks, we propose the use of so-called random edge graph neural networks (REGNNs). Such REG-NNs are shown to exhibit an essential permutation invariance property for the power allocation problem that suggest transference capabilities. In numerical simulations, we validate this suggestion by showing how REGNNs trained on a single ad-hoc network outperform baselines in new randomly drawn networks of growing size.