Stable and Transferable Wireless Resource Allocation Policies via Manifold Neural Networks

TL;DR

This paper introduces Manifold Neural Networks (MNNs) for resource allocation in large wireless networks, demonstrating their stability under system perturbations and superior performance in simulations.

Contribution

It proposes the use of MNNs as a novel policy parametrization for wireless resource allocation and proves their stability under manifold perturbations.

Findings

MNN policies are stable under Laplace-Beltrami operator perturbations.

MNNs outperform baseline methods in numerical simulations.

The approach enables transferable resource allocation policies.

Abstract

We consider the problem of resource allocation in large scale wireless networks. When contextualizing wireless network structures as graphs, we can model the limits of very large wireless systems as manifolds. To solve the problem in the machine learning framework, we propose the use of Manifold Neural Networks (MNNs) as a policy parametrization. In this work, we prove the stability of MNN resource allocation policies under the absolute perturbations to the Laplace-Beltrami operator of the manifold, representing system noise and dynamics present in wireless systems. These results establish the use of MNNs in achieving stable and transferable allocation policies for large scale wireless networks. We verify our results in numerical simulations that show superior performance relative to baseline methods.