Learning Shortest Paths When Data is Scarce

2026-01-07

arXiv.org

AI Summary

This work addresses the challenge of efficient shortest-path planning in scenarios where real-world trajectory data are scarce, by leveraging simulators that exhibit systematic biases. The authors propose a graph Laplacian-regularized bias estimation method that integrates limited real observations, abundant synthetic data, and edge similarity structures within the road network to model smooth simulator-to-reality discrepancies. They establish theoretical guarantees on path suboptimality and devise an active learning strategy applicable even in the absence of initial real-world data. Through finite-sample error analysis and experiments on road networks across multiple cities, the approach demonstrates its ability to closely approximate optimal paths with only a small amount of real data, while providing computable performance certificates.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Digital twins and other simulators are increasingly used to support routing decisions in large-scale networks. However, simulator outputs often exhibit systematic bias, while ground-truth measurements are costly and scarce. We study a stochastic shortest-path problem in which a planner has access to abundant synthetic samples, limited real-world observations, and an edge-similarity structure capturing expected behavioral similarity across links. We model the simulator-to-reality discrepancy as an unknown, edge-specific bias that varies smoothly over the similarity graph, and estimate it using Laplacian-regularized least squares. This approach yields calibrated edge cost estimates even in data-scarce regimes. We establish finite-sample error bounds, translate estimation error into path-level suboptimality guarantees, and propose a computable, data-driven certificate that verifies near-optimality of a candidate route. For cold-start settings without initial real data, we develop a bias-aware active learning algorithm that leverages the simulator and adaptively selects edges to measure until a prescribed accuracy is met. Numerical experiments on multiple road networks and traffic graphs further demonstrate the effectiveness of our methods.

Problem

• shortest path
• data scarcity
• simulator bias
• edge cost estimation
• digital twin

Innovation

• Laplacian regularization
• simulator-to-reality bias
• active learning
• stochastic shortest path
• data-scarce routing