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.

Accelerated Preference Elicitation with LLM-Based Proxies

Bidders in combinatorial auctions face significant challenges when describing their preferences to an auctioneer. Classical work on preference elicitation focuses on query-based techniques inspired from proper learning--often via proxies that interface between bidders and an auction mechanism--to incrementally learn bidder preferences as needed to compute efficient allocations. Although such elicitation mechanisms enjoy theoretical query efficiency, the amount of communication required may still be too cognitively taxing in practice. We propose a family of efficient LLM-based proxy designs for eliciting preferences from bidders using natural language. Our proposed mechanism combines LLM pipelines and DNF-proper-learning techniques to quickly approximate preferences when communication is limited. To validate our approach, we create a testing sandbox for elicitation mechanisms that communicate in natural language. In our experiments, our most promising LLM proxy design reaches approximately efficient outcomes with five times fewer queries than classical proper learning based elicitation mechanisms.