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Dynamic Welfare-Maximizing Pooled Testing

Pooled testing is a common strategy for public health disease screening under limited testing resources, allowing multiple biological samples to be tested together with the resources of a single test, at the cost of reduced individual resolution. While dynamic and adaptive strategies have been extensively studied in the classical pooled testing literature, where the goal is to minimize the number of tests required for full diagnosis of a given population, much of the existing work on welfare-maximizing pooled testing adopts static formulations in which all tests are assigned in advance. In this paper, we study dynamic welfare-maximizing pooled testing strategies in which a limited number of tests are performed sequentially to maximize social welfare, defined as the aggregate utility of individuals who are confirmed to be healthy. We formally define the dynamic problem and study algorithmic approaches for sequential test assignment. Because exact dynamic optimization is computationally infeasible beyond small instances, we evaluate a range of strategies (including exact optimization baselines, greedy heuristics, mixed-integer programming relaxations, and learning-based policies) and empirically characterize their performance and tradeoffs using synthetic experiments. Our results show that dynamic testing can yield substantial welfare improvements over static baselines in low-budget regimes. We find that much of the benefit of dynamic testing is captured by simple greedy policies, which substantially outperform static approaches while remaining computationally efficient. Learning-based methods are included as flexible baselines, but in our experiments they do not reliably improve upon these heuristics. Overall, this work provides a principled computational perspective on dynamic pooled testing and clarifies when dynamic assignment meaningfully improves welfare in public health screening.

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