arXiv:2601.22419cs.GTcs.AI2026-01

动态分批检测可显著提升公共健康筛查的群体福利,尤其在资源有限时。

Dynamic Welfare-Maximizing Pooled Testing

  • 按序动态分配检测资源,逐轮优化测试策略以最大化健康者确认数
  • 低预算下动态策略比静态方案提升近30%的群体福利,且简单贪心算法已接近最优
  • 适合关注资源受限场景下公平性与效率平衡的公共卫生决策者

在检测资源有限的公共健康筛查中,池化检测通过合并多个样本共用一次检测,但会降低个体确诊能力。尽管经典文献多研究最小化总检测数的动态自适应策略,现有福利最大化研究大多采用预先固定检测分配的静态方法。本文首次系统研究动态福利最大化池化检测:在有限检测次数下,通过顺序执行检测以最大化被确认健康的个体总效用。我们构建了该动态问题的形式化框架,并评估多种算法(包括精确优化、贪心启发式、混合整数规划松弛及学习型策略)在合成数据上的表现。结果表明,在低预算条件下,动态策略相比静态基线可实现显著福利提升;其中简单贪心策略已能捕获大部分收益,计算开销极小;学习方法虽具灵活性,但在实验中未稳定超越贪心法。本工作为动态池化检测提供了严谨的计算视角,明确了其在公共卫生筛查中提升群体福祉的有效边界。

原文摘要 · Abstract (English)

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.

池化检测动态优化公共健康福利最大化

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