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引用次数: 25

摘要

图神经网络(gnn)对图数据中的非线性表示进行建模,并应用于分布式代理协调、控制和规划等领域。然而,目前的GNN实现假设了理想的分布式场景,忽略了由于环境或人为因素而发生的链路波动。在这些情况下,如果不相应地考虑拓扑随机性,GNN将无法解决其分布式任务。为了克服这个问题,我们提出了随机图神经网络(SGNN)模型:一个修改分布式图卷积算子以考虑网络变化的GNN。由于随机性带来了一种新的范式,我们开发了一种新的SGNN学习过程,并引入了随机梯度下降(SGD)算法来估计参数。在温和的Lipschitz假设下,我们通过SGD证明了SGNN学习过程收敛于平稳点。数值模拟验证了该理论,并表明在随机时变图上运行时,与传统GNN相比,SGNN具有更好的性能。
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Stochastic Graph Neural Networks
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. However, current GNN implementations assume ideal distributed scenarios and ignore link fluctuations that occur due to environment or human factors. In these situations, the GNN fails to address its distributed task if the topological randomness is not considered accordingly. To overcome this issue, we put forth the stochastic graph neural network (SGNN) model: a GNN where the distributed graph convolutional operator is modified to account for the network changes. Since stochasticity brings in a new paradigm, we develop a novel learning process for the SGNN and introduce the stochastic gradient descent (SGD) algorithm to estimate the parameters. We prove through the SGD that the SGNN learning process converges to a stationary point under mild Lipschitz assumptions. Numerical simulations corroborate the proposed theory and show an improved performance of the SGNN compared with the conventional GNN when operating over random time varying graphs.
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