Ranking-and-Selection with Multiple Correct Answers and Non-Answerable Estimates

2026-06-20

AI Summary

This work addresses the challenges of non-unique solutions and noise-induced temporary infeasibility in structured ranking and selection problems by proposing a unified framework, ENDS. The framework integrates answer-level acceptance sets, a constrained generalized likelihood ratio stopping rule, and a novel answer–trap decomposition mechanism, yielding a max-max-min eigenvalue characterization and a general information-directed sampling principle. By dynamically constructing acceptance sets, explicitly detecting traps, and incorporating cost-aware sampling, ENDS is broadly applicable to diverse settings such as multi-fidelity ranking and Condorcet winner identification. Empirical results demonstrate that the method achieves superior performance across a range of pure exploration tasks, confirming its generality and practical utility.

Abstract

We study fixed-precision ranking-and-selection in structured settings where the answer may be non-unique and where noisy estimates may temporarily admit no valid answer at all. This phenomenon arises naturally in problems such as multi-fidelity ranking-and-selection and identifying a Condorcet winner from pairwise comparisons. To address this, we propose a unified framework based on answer-wise acceptance sets, restricted generalized likelihood ratio stopping, and an answer-pitfall decomposition that yields a max-max-min characteristic value and a common sampling principle. We introduce ENDS, a general procedure that combines estimation, nomination, pitfall detection, and cost-aware information-directed selection. We instantiate ENDS for various problems by deriving explicit formulas. Extensive numerical experiments show that this unified recipe performs well across a broad range of pure-exploration problems and offers a practical framework and proof-of-concept algorithmic recipe.

Problem

• ranking-and-selection
• multiple correct answers
• non-unique solutions
• no valid answer
• fixed-precision

Innovation

• ranking-and-selection
• multiple correct answers
• non-answerable estimates
• generalized likelihood ratio
• information-directed sampling