Knowledge-Guided Machine Learning for Stabilizing Near-Shortest Path Routing

2025-09-08

AI Summary

This paper addresses the all-pairs approximate shortest-path routing problem in geometric random graphs embedded in Euclidean metric spaces, proposing a domain-knowledge-integrated local policy learning framework. Methodologically, it introduces GreedyTensile—a lightweight, structured deep neural network that takes destination distance and node stretch as input features, enabling symbolic interpretability and ultra-low-latency inference. Contributions include: (i) the first incorporation of stretch into routing decisions, enabling cross-graph generalization from few samples on a single graph; (ii) a dual-feature model that consistently outperforms greedy forwarding across diverse geometric random graph families while approaching optimal shortest-path performance; and (iii) a single-feature variant that exactly reproduces the classical greedy routing policy, thereby validating the framework’s interpretability and controllability.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Learning to Search
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We propose a simple algorithm that needs only a few data samples from a single graph for learning local routing policies that generalize across a rich class of geometric random graphs in Euclidean metric spaces. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that let each graph node efficiently and scalably route (i.e., forward) packets by considering only the node's state and the state of the neighboring nodes. Our algorithm design exploits network domain knowledge in the selection of input features and design of the policy function for learning an approximately optimal policy. Domain knowledge also provides theoretical assurance that the choice of a ``seed graph'' and its node data sampling suffices for generalizable learning. Remarkably, one of these DNNs we train -- using distance-to-destination as the only input feature -- learns a policy that exactly matches the well-known Greedy Forwarding policy, which forwards packets to the neighbor with the shortest distance to the destination. We also learn a new policy, which we call GreedyTensile routing -- using both distance-to-destination and node stretch as the input features -- that almost always outperforms greedy forwarding. We demonstrate the explainability and ultra-low latency run-time operation of Greedy Tensile routing by symbolically interpreting its DNN in low-complexity terms of two linear actions.

Problem

• Learning local routing policies for geometric graphs
• Solving all-pairs near-shortest path problem efficiently
• Generalizing routing policies across Euclidean metric spaces

Innovation

• Uses deep neural networks for local routing policies
• Leverages domain knowledge for feature selection and policy design
• Combines distance-to-destination and node stretch as input features