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.

翻译：混合检测是公共卫生疾病筛查在检测资源有限情况下的常用策略，它允许多个生物样本以单个检测的资源消耗进行合并检测，但代价是降低了个体分辨率。尽管经典混合检测文献已广泛研究了动态自适应策略（其目标是在给定人群中以最小检测次数实现完全诊断），但现有关于福利最大化混合检测的研究大多采用静态框架，即所有检测任务均预先分配。本文研究动态福利最大化的混合检测策略：通过顺序执行有限次数的检测来最大化社会福利（定义为被确认健康个体的总效用）。我们正式定义了该动态问题，并研究了顺序检测分配的算法方法。由于精确动态优化在超出小规模实例时计算不可行，我们评估了一系列策略（包括精确优化基线、贪婪启发式算法、混合整数规划松弛及基于学习的策略），并通过合成实验实证分析了其性能与权衡。结果表明，在低预算场景下，动态检测相比静态基线能带来显著的福利提升。我们发现动态检测的大部分优势可通过简单的贪婪策略实现，这些策略在保持计算高效的同时显著优于静态方法。基于学习的方法作为灵活基线被纳入研究，但在我们的实验中未能稳定超越这些启发式算法。总体而言，本研究为动态混合检测提供了理论计算视角，并阐明了动态分配在公共卫生筛查中何时能实质性地提升福利水平。