Optimal Wireless Resource Allocation With Random Edge Graph Neural Networks

We consider the problem of optimally allocating resources across a set of transmitters and receivers in a wireless network. The resulting optimization problem takes the form of constrained statistical learning, in which solutions can be found in a model-free manner by parameterizing the resource allocation policy. Convolutional neural networks architectures are an attractive option for parameterization, as their dimensionality is small and does not scale with network size. We introduce the random edge graph neural network (REGNN), which performs convolutions over random graphs formed by the fading interference patterns in the wireless network. The REGNN-based allocation policies are shown to retain an important permutation equivariance property that makes them amenable to transference to different networks. We further present an unsupervised model-free primal-dual learning algorithm to train the weights of the REGNN. Through numerical simulations, we demonstrate the strong performance REGNNs obtain relative to heuristic benchmarks and their transference capabilities.

I. Introduction

Wireless systems are integral to large scale intelligent systems, from robotics to the Internet of Things (IoT). The design of such systems requires optimal balancing of the numerous utilities and constraints that define the operating point of large networks of wireless connected devices. At a high level, such optimal design problems can be viewed as the allocation of a finite set of resources to achieve strong average performance over the randomly varying wireless channel. While these optimization problems can be easily formulated, they tend to be intractable as they are most often non-convex and infinite dimensional [1]. Some simplification is attained by working in the Lagrangian dual domain  [1], [2] and subsequently using dual descent methods [3]–[5], or, alternatively, with heuristic optimization and scheduling methods [6]–[9].