Technology Category
Planning, Routing, and Scheduling: Planning under UncertaintySearch and Optimization: Heuristic SearchReasoning under Uncertainty: Sequential Decision Making
Bayesian Graph Traversal
🤖 AI Summary
This paper addresses Bayesian path planning on uncertain graphs: a traveler knows only the graph topology and starting node, while edge costs and node rewards are initially unknown and revealed dynamically upon traversal; the objective is to maximize expected utility—defined as the reward from the first visit to a target node minus cumulative traversal cost. We propose the first modeling framework that couples sequential Bayesian decision-making with graph traversal, employing Gaussian process priors to encode uncertainty in edge costs and node rewards, and rigorously prove the problem is NP-hard. We design an exploration-exploitation heuristic strategy with theoretical guarantees and practical efficacy, achieving balanced trade-offs between information gathering and path optimization. Experiments on Erdős–Rényi random graphs and a real-world public-safety drone patrol scenario demonstrate that our method significantly outperforms greedy and random baselines, improving expected utility by 32%–67%.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Develops Bayesian decision strategies for uncertain graph traversal.
Maximizes expected utility with Gaussian process beliefs.
Provides heuristics balancing exploration and exploitation in routing.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Bayesian decision-analytic graph traversal approach
Gaussian process prior for reward and cost beliefs
Heuristics balancing exploration and exploitation
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2024-05-24arXiv.orgCitations: 0
