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

arXiv: https://arxiv.org/abs/2606.21889 · HTML: https://mlsanity.com/paper/2606.21889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 20 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Pure Exploration with Multiple Correct Answers](https://mlsanity.com/paper/1902.03475/) (2019)
- [Admissible anytime-valid sequential inference must rely on nonnegative martingales](https://mlsanity.com/paper/2009.03167/) (2020)
- [Review on Ranking and Selection: A New Perspective](https://mlsanity.com/paper/2008.00249/) (2020)
- [Gradient Ascent for Active Exploration in Bandit Problems](https://mlsanity.com/paper/1905.08165/) (2019)
- [Optimizing Adaptive Experiments: A Unified Approach to Regret Minimization and Best-Arm Identification](https://mlsanity.com/paper/2402.10592/) (2024)
- [The Sample Complexity of Best-k Items Selection from Pairwise Comparisons](https://mlsanity.com/paper/2007.03133/) (2020)
- [Optimal Multi-Fidelity Best-Arm Identification](https://mlsanity.com/paper/2406.03033/) (2024)
- [Combinatorial Pure Exploration of Dueling Bandit](https://mlsanity.com/paper/2006.12772/) (2020)
- [Dual-Directed Algorithm Design for Efficient Pure Exploration](https://mlsanity.com/paper/2310.19319/) (2023)

## Abstract (arXiv)

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.