Zaile Li

Zaile Li, Weiwei Fan, L. Jeff Hong

Screening tasks that aim to identify a small subset of top alternatives from a large pool are common in business decision-making processes. These tasks often require substantial human effort to evaluate each alternative's performance, making them time-consuming and costly. Motivated by recent advances in large language models (LLMs), particularly their ability to generate outputs that align well with human evaluations, we consider an LLM-as-human-evaluator approach for conducting screening virtually, thereby reducing the cost burden. To achieve scalability and cost-effectiveness in virtual screening, we identify that the stochastic nature of LLM outputs and their cost structure necessitate efficient budget allocation across all alternatives. To address this, we propose using a top-$m$ greedy evaluation mechanism, a simple yet effective approach that keeps evaluating the current top-$m$ alternatives, and design the explore-first top-$m$ greedy (EFG-$m$) algorithm. We prove that EFG-$m$ is both sample-optimal and consistent in large-scale virtual screening. Surprisingly, we also uncover a bonus ranking effect, where the algorithm naturally induces an indifference-based ranking within the selected subset. To further enhance practicality, we design a suite of algorithm variants to improve screening performance and computational efficiency. Numerical experiments validate our results and demonstrate the effectiveness of our algorithms. Lastly, we conduct a case study on LLM-based virtual screening. The study shows that while LLMs alone may not provide meaningful screening and ranking results when directly queried, integrating them with our sample-optimal algorithms unlocks their potential for cost-effective, large-scale virtual screening.

Zaile Li, Weiwei Fan, L. Jeff Hong

Selecting the best alternative from a finite set represents a broad class of pure exploration problems. Traditional approaches to pure exploration have predominantly relied on Gaussian or sub-Gaussian assumptions on the performance distributions of all alternatives, which limit their applicability to non-sub-Gaussian especially heavy-tailed problems. The need to move beyond sub-Gaussianity may become even more critical in large-scale problems, which tend to be especially sensitive to distributional specifications. In this paper, motivated by the widespread use of upper confidence bound (UCB) algorithms in pure exploration and beyond, we investigate their performance in the large-scale, non-sub-Gaussian settings. We consider the simplest category of UCB algorithms, where the UCB value for each alternative is defined as the sample mean plus an exploration bonus that depends only on its own sample size. We abstract this into a meta-UCB algorithm and propose letting it select the alternative with the largest sample size as the best upon stopping. For this meta-UCB algorithm, we first derive a distribution-free lower bound on the probability of correct selection. Building on this bound, we analyze two general non-sub-Gaussian scenarios: (1) all alternatives follow a common location-scale structure and have bounded variance; and (2) when such a structure does not hold, each alternative has a bounded absolute moment of order $q > 3$. In both settings, we show that the meta-UCB algorithm and therefore a broad class of UCB algorithms can achieve the sample optimality. These results demonstrate the applicability of UCB algorithms for solving large-scale pure exploration problems with non-sub-Gaussian distributions. Numerical experiments support our results and provide additional insights into the comparative behaviors of UCB algorithms within and beyond our meta-UCB framework.

Zaile Li, Yuchen Wan, L. Jeff Hong

Ranking and selection (R&S) aims to identify the alternative with the best mean performance among $k$ simulated alternatives. The practical value of R&S depends on accurate simulation input modeling, which often suffers from the curse of input uncertainty due to limited data. Distributionally robust ranking and selection (DRR&S) addresses this challenge by modeling input uncertainty via an ambiguity set of $m > 1$ plausible input distributions, resulting in $km$ scenarios in total. Recent DRR&S studies suggest a key structural insight: additivity in budget allocation is essential for efficiency. However, existing justifications are heuristic, and fundamental properties such as consistency and the precise allocation pattern induced by additivity remain poorly understood. In this paper, we propose a simple additive allocation (AA) procedure that aims to exclusively sample the $k + m - 1$ previously hypothesized critical scenarios. Leveraging boundary-crossing arguments, we establish a lower bound on the probability of correct selection and characterize the procedure's budget allocation behavior. We then prove that AA is consistent and, surprisingly, achieves additivity in the strongest sense: as the total budget increases, only $k + m - 1$ scenarios are sampled infinitely often. Notably, the worst-case scenarios of non-best alternatives may not be among them, challenging prior beliefs about their criticality. These results offer new and counterintuitive insights into the additive structure of DRR&S. To improve practical performance while preserving this structure, we introduce a general additive allocation (GAA) framework that flexibly incorporates sampling rules from traditional R&S procedures in a modular fashion. Numerical experiments support our theoretical findings and demonstrate the competitive performance of the proposed GAA procedures.