Adaptive Frontier Exploration on Graphs with Applications to Network-Based Disease Testing

• URL: http://arxiv.org/abs/2505.21671v1
• Date: Tue, 27 May 2025 18:48:42 GMT
• Title: Adaptive Frontier Exploration on Graphs with Applications to Network-Based Disease Testing
• Authors: Davin Choo, Yuqi Pan, Tonghan Wang, Milind Tambe, Alastair van Heerden, Cheryl Johnson,
• Abstract summary: We study a sequential decision-making problem on a $n$-node graph $G$ where each node has an unknown label.<n>We design a Gittins index-based policy that applies to general graphs and is provably optimal when $G$ is a forest.<n>Experiments on synthetic and real-world graphs show that our method consistently outperforms natural baselines.
• Score: 25.36924544001149
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a sequential decision-making problem on a $n$-node graph $G$ where each node has an unknown label from a finite set $\mathbf{\Sigma}$, drawn from a joint distribution $P$ that is Markov with respect to $G$. 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 $G$ is a forest. Our implementation runs in $O(n^2 \cdot |\mathbf{\Sigma}|^2)$ time while using $O(n \cdot |\mathbf{\Sigma}|^2)$ oracle calls to $P$ and $O(n^2 \cdot |\mathbf{\Sigma}|)$ 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.

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