We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that efficiently and scalably learn routing policies that are local, i.e., they only consider node states and the states of neighboring nodes. Remarkably, one of these DNNs we train learns a policy that exactly matches the performance of greedy forwarding; another generally outperforms greedy forwarding. Our algorithm design exploits network domain knowledge in several ways: First, in the selection of input features and, second, in the selection of a ``seed graph'' and subsamples from its shortest paths. The leverage of domain knowledge provides theoretical explainability of why the seed graph and node subsampling suffice for learning that is efficient, scalable, and generalizable. Simulation-based results on uniform random graphs with diverse sizes and densities empirically corroborate that using samples generated from a few routing paths in a modest-sized seed graph quickly learns a model that is generalizable across (almost) all random graphs in the wireless network model.

翻译：我们提出了一种用于局部路由策略的学习算法，该算法仅需从单个图中获取少量数据样本，即可泛化至无线网络标准模型中的所有随机图。由此，我们通过训练深度神经网络（DNN）解决了全对近最短路径问题，这些网络能够高效且可扩展地学习局部路由策略，即仅考虑节点状态及其邻居节点的状态。值得注意的是，我们训练的其中一个DNN学习到的策略与贪婪转发的性能完全匹配；另一个则普遍优于贪婪转发。我们的算法设计在多个方面利用了网络领域知识：首先，在输入特征的选择上；其次，在选择“种子图”及其最短路径的子样本时。领域知识的运用从理论上解释了为何种子图和节点子采样足以实现高效、可扩展且可泛化的学习。基于不同规模和密度的均匀随机图的仿真结果实证表明，利用中等规模种子图中少量路由路径生成的样本，能够快速训练出一个可泛化至无线网络模型中（几乎）所有随机图的模型。