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Graph Neural Networks for Scalable Radio Resource Management Architecture Design and Theoretical Analysis

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Document pages: 14 pages

Abstract: Deep learning has recently emerged as a disruptive technology to solvechallenging radio resource management problems in wireless networks. However,the neural network architectures adopted by existing works suffer from poorscalability, generalization, and lack of interpretability. A long-standingapproach to improve scalability and generalization is to incorporate thestructures of the target task into the neural network architecture. In thispaper, we propose to apply graph neural networks (GNNs) to solve large-scaleradio resource management problems, supported by effective neural networkarchitecture design and theoretical analysis. Specifically, we firstdemonstrate that radio resource management problems can be formulated as graphoptimization problems that enjoy a universal permutation equivariance property.We then identify a class of neural networks, named emph{message passing graphneural networks} (MPGNNs). It is demonstrated that they not only satisfy thepermutation equivariance property, but also can generalize to large-scaleproblems while enjoying a high computational efficiency. For interpretablityand theoretical guarantees, we prove the equivalence between MPGNNs and a classof distributed optimization algorithms, which is then used to analyze theperformance and generalization of MPGNN-based methods. Extensive simulations,with power control and beamforming as two examples, will demonstrate that theproposed method, trained in an unsupervised manner with unlabeled samples,matches or even outperforms classic optimization-based algorithms withoutdomain-specific knowledge. Remarkably, the proposed method is highly scalableand can solve the beamforming problem in an interference channel with $1000$transceiver pairs within $6$ milliseconds on a single GPU.

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