Policy-Embedded Graph Expansion: Networked HIV Testing with Diffusion-Driven Network Samples

HIV is a retrovirus that attacks the human immune system and can lead to death without proper treatment. In collaboration with the WHO and Wits University, we study how to improve the efficiency of HIV testing with the goal of eventual deployment, directly supporting progress toward UN Sustainable Development Goal 3.3. While prior work has demonstrated the promise of intelligent algorithms for sequential, network-based HIV testing, existing approaches rely on assumptions that are impractical in our real-world implementations. Here, we study sequential testing on incrementally revealed disease networks and introduce Policy-Embedded Graph Expansion (PEGE), a novel framework that directly embeds a generative distribution over graph expansions into the decision-making policy rather than attempting explicit topological reconstruction. We further propose Dynamics-Driven Branching (DDB), a diffusion-based graph expansion model that supports decision making in PEGE and is designed for data-limited settings where forest structures arise naturally, as in our real-world referral process. Experiments on real HIV transmission networks show that the combined approach (PEGE + DDB) consistently outperforms existing baselines (e.g., 13% improvement in discounted reward and 9% more HIV detections with 25% of the population tested) and explore key tradeoffs that drive decision quality.

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

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.