解决多正确答案与无解估计的排序选择难题
Ranking-and-Selection with Multiple Correct Answers and Non-Answerable Estimates
- 基于答案级接受集构建统一框架
- 在多种问题中实现高效稳定的选择性能
- 适合需要可靠排序的工程与决策场景
我们研究结构化环境下的固定精度排序与选择问题，其中答案可能不唯一，且噪声估计可能暂时无有效解。这类现象自然出现在多保真度排序选择和成对比较中寻找康多塞胜者等问题中。为此，我们提出一个统一框架，包含答案级接受集、受限广义似然比停止规则，以及答案陷阱分解，导出最大-最大-最小特征值和通用采样原则。我们引入ENDS，一种结合估计、提名、陷阱检测与成本感知信息导向选择的通用算法。通过推导显式公式，将ENDS应用于多种问题。大量数值实验表明，该统一方法在广泛的纯探索问题中表现良好，提供了一个实用的框架和概念验证算法。
原文摘要 · Abstract (English)
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.
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