Bayesian Graph Traversal
Document Type
Article
Publication Date
10-1-2025
Abstract
This research considers Bayesian decision-analytic approaches toward the traversal of an uncertain graph. Namely, a traveler progresses over a graph in which rewards are gained upon a node’s first visit, and costs are incurred for every edge traversal. The traveler knows the graph’s adjacency matrix and the starting position but does not know the rewards and costs. The traveler is a Bayesian who encodes his beliefs about these values using a Gaussian process prior and who seeks to maximize his expected utility over these beliefs. Adopting a decision-analytic perspective, we develop sequential decision-making solution strategies for this coupled information-collection and network-routing problem. We show that the problem is NP-hard and derive properties of the optimal walk. These properties provide heuristics for the traveler’s problem that balance exploration and exploitation. We provide a practical case study focused on the use of unmanned aerial systems for public safety and empirically study policy performance in myriad Erdös–Rényi settings.
Source Publication
Decision Analysis (ISSN 1545-8490 | eISSN 1545-8504)
Recommended Citation
Caballero, W. N., Jenkins, P. R., Banks, D., & Robbins, M. (2026). Bayesian graph traversal. Decision Analysis, 23(1), 11–27. https://doi.org/10.1287/deca.2024.0239
Comments
This article is available from the publisher, INFORMS, by subscrption or purchase using the DOI link below.
The article was published online in October 2025 ahead of the March 2026 issue.
Funding: This work was supported by the Office of Naval Research [Grant 6000012277] and the Air Force Office of Scientific Research [Grant 21RT0867].