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

2025-05-27

AI Summary

This paper studies adaptive sequential exploration on graphs under frontier constraints: node labels are unknown and follow a graph Markov random field; at each step, only neighbors of already-selected nodes can be queried; the objective is to maximize discounted cumulative reward. We are the first to adapt the Gittins index policy to this frontier-restricted setting, proving its optimality on forest graphs and extending it theoretically to general graphs. We further propose an efficient approximation algorithm with provable guarantees. Our method integrates graph Markov modeling, neighborhood-constrained dynamic programming, and probabilistic inference, supporting oracle-based optimization. In HIV contact-tracing simulations, our approach identifies nearly 100% of positive cases by screening only 50% of the population—substantially outperforming baselines. The algorithm runs in O(n²|Σ|²) time, enabling scalability to large-scale graphs.

Technology Category

• Search and Optimization: Heuristic Search
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Maximize rewards by adaptively selecting nodes on a graph
• Explore graph frontiers under neighbor-only action constraints
• Optimize disease testing via contact tracing network strategies

Innovation

• Gittins index-based policy for graph exploration
• Optimal for forest-structured graphs
• Efficient implementation with O(n^2) complexity