Learning Resource Allocation Policy: Vertex-GNN or Edge-GNN?

TL;DR

This paper analyzes the expressive power of Vertex-GNNs and Edge-GNNs in learning wireless resource allocation policies, revealing that Edge-GNNs generally outperform Vertex-GNNs in differentiating channel information and efficiency.

Contribution

The paper provides a theoretical analysis of GNN expressive power for wireless policies and demonstrates Edge-GNNs' advantages over Vertex-GNNs through simulations.

Findings

Edge-GNNs can differentiate all channel matrices with linear processors.

Vertex-GNNs struggle with channel differentiation when using linear processors.

Edge-GNNs achieve comparable performance with lower training and inference time.

Abstract

Graph neural networks (GNNs) update the hidden representations of vertices (called Vertex-GNNs) or hidden representations of edges (called Edge-GNNs) by processing and pooling the information of neighboring vertices and edges and combining to exploit topology information. When learning resource allocation policies, GNNs cannot perform well if their expressive power is weak, i.e., if they cannot differentiate all input features such as channel matrices. In this paper, we analyze the expressive power of the Vertex-GNNs and Edge-GNNs for learning three representative wireless policies: link scheduling, power control, and precoding policies. We find that the expressive power of the GNNs depends on the linearity and output dimensions of the processing and combination functions. When linear processors are used, the Vertex-GNNs cannot differentiate all channel matrices due to the loss of channel information, while the Edge-GNNs can. When learning the precoding policy, even the Vertex-GNNs with non-linear processors may not be with strong expressive ability due to the dimension compression. We proceed to provide necessary conditions for the GNNs to well learn the precoding policy. Simulation results validate the analyses and show that the Edge-GNNs can achieve the same performance as the Vertex-GNNs with much lower training and inference time.