The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the unknown interaction model. Besides, high-dimensional and nonlinear state trajectories make difficult to identify if two nodes are connected. Current solutions rely on prior knowledge of the graph topology and the dynamic behavior of the nodes, and hence, have poor generalization to other network configurations. To address these issues, we propose a novel learning-based approach that combines (i) a strongly convex program that efficiently uncovers graph topologies with global convergence guarantees and (ii) a self-attention encoder that learns to embed the original state trajectories into a feature space and predicts appropriate regularizers for the optimization program. In contrast to other works, our approach can identify the graph topology of unseen networks with new configurations in terms of number of nodes, connectivity or state trajectories. We demonstrate the effectiveness of our approach in identifying graphs in multi-robot formation and flocking tasks.

翻译：图识别问题旨在根据网络中节点的状态/特征轨迹发现节点间的交互关系。该问题具有挑战性，因为节点的行为通过未知交互模型与其他所有节点耦合。此外，高维非线性状态轨迹使得难以判断两个节点是否相连。现有解决方案依赖于图拓扑结构和节点动态行为的先验知识，因此对其他网络配置的泛化能力较差。为解决这些问题，我们提出一种新颖的基于学习的方法，该方法结合了：(i) 一个强凸优化程序，可高效揭示图拓扑结构并具有全局收敛性保证；(ii) 一个自注意力编码器，学习将原始状态轨迹嵌入到特征空间并为优化程序预测合适的正则化项。与现有工作不同，我们的方法能够识别具有新配置（包括节点数量、连通性或状态轨迹）的未见网络的图拓扑结构。我们通过多机器人编队和集群任务中的图识别实验证明了该方法的有效性。