论文标题
使用图神经网络进行资源分配的尺寸概括
Size Generalization for Resource Allocation with Graph Neural Networks
论文作者
论文摘要
尺寸的概括对于学习无线策略很重要,这通常具有动态大小,例如由时间变化的用户引起的。学习以优化资源分配的最新研究作品表明,图形神经网络(GNN)可以推广到不同的问题量表。但是,GNN不能保证跨输入尺寸概括。在本文中,我们努力分析GNNS的尺寸泛化机制时,学习置换式(PE)策略。我们发现,GNN的聚合函数和激活函数在其大小的泛化能力上起关键作用。我们以平均聚合器(称为Mean-gnn)为示例以证明大小的泛化条件,并解释为什么无线通信文献中的几个GNN可以很好地推广到问题量表。为了说明如何根据我们的发现设计具有尺寸概括性的GNN,我们考虑了功率和带宽分配,并建议在Mean-gnn的输出层中选择或预训练激活函数以学习PE策略。仿真结果表明,所提出的GNN可以很好地概括为用户的数量,这可以验证我们在学习PE策略时对GNN的大小概括条件的分析。
Size generalization is important for learning wireless policies, which are often with dynamic sizes, say caused by time-varying number of users. Recent works of learning to optimize resource allocation empirically demonstrate that graph neural networks (GNNs) can generalize to different problem scales. However, GNNs are not guaranteed to generalize across input sizes. In this paper, we strive to analyze the size generalization mechanism of GNNs when learning permutation equivariant (PE) policies. We find that the aggregation function and activation functions of a GNN play a key role on its size generalization ability. We take the GNN with mean aggregator, called mean-GNN, as an example to demonstrate a size generalization condition, and interpret why several GNNs in the literature of wireless communications can generalize well to problem scales. To illustrate how to design GNNs with size generalizability according to our finding, we consider power and bandwidth allocation, and suggest to select or pre-train activation function in the output layer of mean-GNN for learning the PE policies. Simulation results show that the proposed GNN can generalize well to the number of users, which validate our analysis for the size generalization condition of GNNs when learning the PE policies.