Adaptive Frontier Exploration on Graphs with Applications to Network-Based Disease Testing
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arXiv
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| Format: | Preprint |
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2025
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| author | Choo, Davin Pan, Yuqi Wang, Tonghan Tambe, Milind van Heerden, Alastair Johnson, Cheryl |
| author_facet | Choo, Davin Pan, Yuqi Wang, Tonghan Tambe, Milind van Heerden, Alastair Johnson, Cheryl |
| contents | We study a sequential decision-making problem on a $n$-node graph $\mathcal{G}$ where each node has an unknown label from a finite set $\mathbfΩ$, drawn from a joint distribution $\mathcal{P}$ that is Markov with respect to $\mathcal{G}$. At each step, selecting a node reveals its label and yields a label-dependent reward. The goal is to adaptively choose nodes to maximize expected accumulated discounted rewards. We impose a frontier exploration constraint, where actions are limited to neighbors of previously selected nodes, reflecting practical constraints in settings such as contact tracing and robotic exploration. We design a Gittins index-based policy that applies to general graphs and is provably optimal when $\mathcal{G}$ is a forest. Our implementation runs in $\mathcal{O}(n^2 \cdot |\mathbfΩ|^2)$ time while using $\mathcal{O}(n \cdot |\mathbfΩ|^2)$ oracle calls to $\mathcal{P}$ and $\mathcal{O}(n^2 \cdot |\mathbfΩ|)$ space. Experiments on synthetic and real-world graphs show that our method consistently outperforms natural baselines, including in non-tree, budget-limited, and undiscounted settings. For example, in HIV testing simulations on real-world sexual interaction networks, our policy detects nearly all positive cases with only half the population tested, substantially outperforming other baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21671 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Frontier Exploration on Graphs with Applications to Network-Based Disease Testing Choo, Davin Pan, Yuqi Wang, Tonghan Tambe, Milind van Heerden, Alastair Johnson, Cheryl Artificial Intelligence Data Structures and Algorithms Machine Learning Optimization and Control We study a sequential decision-making problem on a $n$-node graph $\mathcal{G}$ where each node has an unknown label from a finite set $\mathbfΩ$, drawn from a joint distribution $\mathcal{P}$ that is Markov with respect to $\mathcal{G}$. At each step, selecting a node reveals its label and yields a label-dependent reward. The goal is to adaptively choose nodes to maximize expected accumulated discounted rewards. We impose a frontier exploration constraint, where actions are limited to neighbors of previously selected nodes, reflecting practical constraints in settings such as contact tracing and robotic exploration. We design a Gittins index-based policy that applies to general graphs and is provably optimal when $\mathcal{G}$ is a forest. Our implementation runs in $\mathcal{O}(n^2 \cdot |\mathbfΩ|^2)$ time while using $\mathcal{O}(n \cdot |\mathbfΩ|^2)$ oracle calls to $\mathcal{P}$ and $\mathcal{O}(n^2 \cdot |\mathbfΩ|)$ space. Experiments on synthetic and real-world graphs show that our method consistently outperforms natural baselines, including in non-tree, budget-limited, and undiscounted settings. For example, in HIV testing simulations on real-world sexual interaction networks, our policy detects nearly all positive cases with only half the population tested, substantially outperforming other baselines. |
| title | Adaptive Frontier Exploration on Graphs with Applications to Network-Based Disease Testing |
| topic | Artificial Intelligence Data Structures and Algorithms Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2505.21671 |