# Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks

**Authors:** Mark Eisen, Alejandro Ribeiro  
**arXiv:** [1909.01865](https://arxiv.org/abs/1909.01865)  
**Date:** 2019-09-04  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1909.01865v1/

## Key points

- Study title: "Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks"
- Authors: Mark Eisen and Alejandro Ribeiro
- Problem addressed: Efficient resource allocation in wireless networks
- Proposed approach: Constrained statistical learning with parameterized resource allocation policy
- Parameterization method: Convolutional neural networks (CNNs)
- Introduction of random edge graph neural network (REGNN)
- REGNN performs convolutions over random graphs formed by fading interference patterns
- Allocation policies based on REGNN have permutation equivariance property
- Unsupervised model-free primal-dual learning algorithm to train REGNN weights
- Algorithm allows for efficient optimization without labeled data or manual hyperparameter tuning
- Numerical simulations demonstrate REGNN outperforms heuristic benchmarks in performance and scalability
- Highlighted ability of REGNN to transfer learned policies to different networks successfully
- Potential applications in improving efficiency and performance in wireless communication scenarios.

## Summary

In the study titled "Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks," authors Mark Eisen and Alejandro Ribeiro address the problem of efficiently allocating resources in a wireless network. They propose a constrained statistical learning approach to find optimal solutions by parameterizing the resource allocation policy. Convolutional neural networks (CNNs) are chosen as an attractive option for parameterization due to their small dimensionality, which does not scale with network size. To tackle this problem, the authors introduce the random edge graph neural network (REGNN). REGNN performs convolutions over random graphs formed by the fading interference patterns in the wireless network. These allocation policies based on REGNN retain an important property called permutation equivariance, making them adaptable to different networks. Additionally, the authors present an unsupervised model-free primal-dual learning algorithm to train the weights of REGNN. This algorithm allows for efficient optimization without requiring labeled data or manual tuning of hyperparameters. Through numerical simulations, the authors demonstrate that REGNNs outperform heuristic benchmarks in terms of performance and scalability. Moreover, they highlight REGNN's ability to transfer its learned policies to different networks successfully. Overall, this study provides valuable insights into optimizing resource allocation in wireless networks using CNN-based approaches like REGNN. The proposed method shows promising results and has potential applications in improving efficiency and performance in various wireless communication scenarios.