Learning Shortest Paths When Data is Scarce

TL;DR

This paper introduces a method to accurately estimate shortest paths in large networks using limited real data, synthetic samples, and a smooth bias model, with theoretical guarantees and active learning strategies.

Contribution

It proposes a Laplacian-regularized bias estimation approach, finite-sample error bounds, and an active learning algorithm for data-efficient routing in scarce data scenarios.

Findings

Effective bias calibration in data-scarce regimes

Theoretical error bounds and suboptimality guarantees

Successful experiments on road and traffic networks

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.