Bayesian Graph Traversal
This work addresses a coupled information-collection and network-routing problem, such as for unmanned aerial systems in public safety, but is incremental as it builds on existing Bayesian and graph traversal methods.
The research tackled the problem of traversing an uncertain graph with unknown rewards and costs using Bayesian decision-analytic approaches, resulting in the development of sequential decision-making strategies and heuristics that balance exploration and exploitation, with empirical performance studied in Erdos-Renyi settings.
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.