论文标题
设计具有无线资源分配的所需排列属性的异质GNN
Designing Heterogeneous GNNs with Desired Permutation Properties for Wireless Resource Allocation
论文作者
论文摘要
图形神经网络(GNN)旨在学习各种无线策略,即从环境参数到决策变量的映射,这要归功于它们的出色性能,并具有启用可伸缩性和尺寸概括性的潜力。这些优点植根于利用置换先验的利用,即满足要学习的策略的置换属性(称为所需的置换属性)。许多无线策略具有复杂的置换属性。为了满足这些特性,应使用异质GNN(HETGNN)来学习此类政策。有两个关键因素使HETGNN能够满足所需的置换属性:构建合适的异质图并明智地设计HetGnn的体系结构。但是,迄今为止,图和HETGNN都在启发式上设计。在本文中,我们努力为设计提供一种系统的方法来满足所需的排列属性。我们首先提出了一种构造策略图的方法,其中为满足复杂的排列属性而定义了边缘及其类型。然后,我们提供并证明了三个足够的条件来设计HETGNN,以便在通过适当的图表学习时可以满足所需的排列属性。这些条件提出了一种通过根据图的顶点和边缘的类型共享处理,组合和汇总功能来设计具有所需置换属性的HETGNN的方法。我们将功率分配和混合预编码策略作为演示如何应用所提出的方法并通过模拟验证置换的影响的示例。
Graph neural networks (GNNs) have been designed for learning a variety of wireless policies, i.e., the mappings from environment parameters to decision variables, thanks to their superior performance, and the potential in enabling scalability and size generalizability. These merits are rooted in leveraging permutation prior, i.e., satisfying the permutation property of the policy to be learned (referred to as desired permutation property). Many wireless policies are with complicated permutation properties. To satisfy these properties, heterogeneous GNNs (HetGNNs) should be used to learn such policies. There are two critical factors that enable a HetGNN to satisfy a desired permutation property: constructing an appropriate heterogeneous graph and judiciously designing the architecture of the HetGNN. However, both the graph and the HetGNN are designed heuristically so far. In this paper, we strive to provide a systematic approach for the design to satisfy the desired permutation property. We first propose a method for constructing a graph for a policy, where the edges and their types are defined for the sake of satisfying complicated permutation properties. Then, we provide and prove three sufficient conditions to design a HetGNN such that it can satisfy the desired permutation property when learning over an appropriate graph. These conditions suggest a method of designing the HetGNN with desired permutation property by sharing the processing, combining, and pooling functions according to the types of vertices and edges of the graph. We take power allocation and hybrid precoding policies as examples for demonstrating how to apply the proposed methods and validating the impact of the permutation prior by simulations.