Deep learning has recently emerged as a disruptive technology to solve challenging radio resource management problems in wireless networks. However, the neural network architectures adopted by existing works suffer from poor scalability and generalization, and lack of interpretability. A long-standing approach to improve scalability and generalization is to incorporate the structures of the target task into the neural network architecture. In this paper, we propose to apply graph neural networks (GNNs) to solve large-scale radio resource management problems, supported by effective neural network architecture design and theoretical analysis. Specifically, we first demonstrate that radio resource management problems can be formulated as graph optimization problems that enjoy a universal permutation equivariance property. We then identify a family of neural networks, named message passing graph neural networks (MPGNNs). It is demonstrated that they not only satisfy the permutation equivariance property, but also can generalize to large-scale problems, while enjoying a high computational efficiency. For interpretablity and theoretical guarantees, we prove the equivalence between MPGNNs and a family of distributed optimization algorithms, which is then used to analyze the performance and generalization of MPGNN-based methods. Extensive simulations, with power control and beamforming as two examples, demonstrate that the proposed method, trained in an unsupervised manner with unlabeled samples, matches or even outperforms classic optimization-based algorithms without domain-specific knowledge. Remarkably, the proposed method is highly scalable and can solve the beamforming problem in an interference channel with 1000 transceiver pairs within 6 milliseconds on a single GPU.

中文翻译：

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用于可扩展无线电资源管理的图神经网络：架构设计和理论分析


深度学习最近已成为解决无线网络中具有挑战性的无线电资源管理问题的颠覆性技术。然而，现有作品采用的神经网络架构的可扩展性和泛化性较差，并且缺乏可解释性。提高可扩展性和泛化性的一个长期存在的方法是将目标任务的结构合并到神经网络架构中。在本文中，我们建议在有效的神经网络架构设计和理论分析的支持下，应用图神经网络（GNN）来解决大规模无线电资源管理问题。具体来说，我们首先证明无线电资源管理问题可以表述为具有通用排列等方差性质的图优化问题。然后，我们确定了一系列神经网络，称为消息传递图神经网络（MPGNN）。事实证明，它们不仅满足排列等方差性质，而且可以推广到大规模问题，同时具有较高的计算效率。为了可解释性和理论保证，我们证明了 MPGNN 和一系列分布式优化算法之间的等价性，然后用于分析基于 MPGNN 的方法的性能和泛化。以功率控制和波束成形为例的广泛模拟表明，所提出的方法以无监督方式使用未标记样本进行训练，可以匹配甚至优于基于经典优化的算法，而无需特定领域的知识。值得注意的是，所提出的方法具有高度可扩展性，可以在单个 GPU 上在 6 毫秒内解决具有 1000 个收发器对的干扰信道中的波束成形问题。