Bayesian Graph Traversal
William N. Caballero, Phillip R. Jenkins, David Banks, Matthew Robbins
TL;DR
The paper addresses planning a Bayesian traversal on an uncertain graph where edge costs and node rewards are unknown and learned via Gaussian process priors. It formulates the problem in a sequential decision framework, derives GP-based posterior updates, and proves NP-hardness, motivating practical heuristics. Four policies—Myopic, UCB, H-Path, and Speculating Clairvoyant—balance exploration and exploitation and are evaluated through illustrative and UAS-public-safety case studies as well as random Erdős–Rényi networks. The results show that H-Path and Speculating Clairvoyant often outperform the baseline while the best choice depends on graph structure and hyperparameters, highlighting the need for problem-aware policy tuning and future extensions. The work advances decision-analytic routing under uncertainty with practical implications for autonomous exploration and information gathering on networks.
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 his 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 Erdos-Renyi settings.