arXiv subjects

Zaile Li

Publications and source records attributed to Zaile Li.

5 recordsLinked to original sources

arXiv2025

UCB for Large-Scale Pure Exploration: Beyond Sub-Gaussianity

Selecting the best alternative from a finite set is the central objective of ranking and selection (R&S) and best arm identification (BAI). Traditional R&S or BAI approaches 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 sequential decision making, we investigate their performance in large-scale, non-sub-Gaussian R&S 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 first study the indifference-zone formulation and show that the meta-UCB algorithm---and therefore a broad class of UCB algorithms---achieves sample optimality as long as the variances are uniformly bounded. We then extend sample optimality to a non-indifference-zone configuration with polynomially shrinking mean gaps under the same variance assumption. These results demonstrate the applicability of UCB algorithms to large-scale R&S 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.

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arXiv2025

Sequential Additivity in Distributionally Robust Ranking and Selection

Ranking and selection (R&S) seeks to identify the alternative with the best mean performance from a finite collection of simulated alternatives. Its practical value depends on accurate simulation input modeling, which is often hindered by input uncertainty arising from limited data. Distributionally robust R&S (DRR&S) addresses this challenge by considering several plausible input distributions and selecting the alternative with the best worst-case mean performance, resulting in a multiplicative number of scenarios. Existing static and oracle analyses suggest that efficient sampling should instead be additive, concentrating on only a small number of critical scenarios. We introduce sequential additivity, which characterizes how this structure emerges from adaptive sequential procedures. We first establish an algorithm-independent sampling lower bound: any consistent DRR&S procedure must sample at least this additive number of scenarios infinitely often. We then study a simplified additive allocation (AA) procedure abstracted from practical sequential designs. Using boundary-crossing arguments, we derive a finite-budget upper bound on its probability of incorrect selection and show that this probability decays exponentially as the budget grows. Moreover, AA attains the necessary sampling lower bound exactly, showing that additivity can be achieved in the strongest possible sense. Surprisingly, the scenarios sampled infinitely often need not be the true worst-case scenarios, showing that worst-case scenario identification may not be necessary for sufficient exploration in DRR&S. To generalize these insights, we introduce a general additive allocation (GAA) framework that incorporates sampling rules from traditional R&S in a modular fashion. Under suitable exploration conditions, GAA procedures retain the key properties of AA.

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arXiv2024

New Additive OCBA Procedures for Robust Ranking and Selection

Robust ranking and selection (R&S) is an important and challenging variation of conventional R&S that seeks to select the best alternative among a finite set of alternatives. It captures the common input uncertainty in the simulation model by using an ambiguity set to include multiple possible input distributions and shifts to select the best alternative with the smallest worst-case mean performance over the ambiguity set. In this paper, we aim at developing new fixed-budget robust R&S procedures to minimize the probability of incorrect selection (PICS) under a limited sampling budget. Inspired by an additive upper bound of the PICS, we derive a new asymptotically optimal solution to the budget allocation problem. Accordingly, we design a new sequential optimal computing budget allocation (OCBA) procedure to solve robust R&S problems efficiently. We then conduct a comprehensive numerical study to verify the superiority of our robust OCBA procedure over existing ones. The numerical study also provides insights on the budget allocation behaviors that lead to enhanced efficiency.

stat.ME↗

arXiv2024

Efficient Budget Allocation for Large-Scale LLM-Enabled Virtual Screening

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.

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arXiv2023

The (Surprising) Sample Optimality of Greedy Procedures for Large-Scale Ranking and Selection

Ranking and selection (R&S) aims to select the best alternative with the largest mean performance from a finite set of alternatives. Recently, considerable attention has turned towards the large-scale R&S problem which involves a large number of alternatives. Ideal large-scale R&S procedures should be sample optimal, i.e., the total sample size required to deliver an asymptotically non-zero probability of correct selection (PCS) grows at the minimal order (linear order) in the number of alternatives, $k$. Surprisingly, we discover that the na\"ive greedy procedure, which keeps sampling the alternative with the largest running average, performs strikingly well and appears sample optimal. To understand this discovery, we develop a new boundary-crossing perspective and prove that the greedy procedure is sample optimal for the scenarios where the best mean maintains at least a positive constant away from all other means as $k$ increases. We further show that the derived PCS lower bound is asymptotically tight for the slippage configuration of means with a common variance. For other scenarios, we consider the probability of good selection and find that the result depends on the growth behavior of the number of good alternatives: if it remains bounded as $k$ increases, the sample optimality still holds; otherwise, the result may change. Moreover, we propose the explore-first greedy procedures by adding an exploration phase to the greedy procedure. The procedures are proven to be sample optimal and consistent under the same assumptions. Last, we numerically investigate the performance of our greedy procedures in solving large-scale R&S problems.

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