2025/10/09 by Kim, Sanghwa, Dohyun Ahn, Ahn, Dohyun +2
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.2510.07862
openalex publication_date 2025/10/09 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
We study the problem of estimating a continuous ability parameter from sequential binary responses by actively asking questions with varying difficulties, a setting that arises naturally in adaptive testing and online preference learning. Our goal is to certify that the estimate lies within a desired margin of error, using as few queries as possible. We propose a simple algorithm that adaptively selects questions to maximize Fisher information and updates the estimate using a method-of-moments approach, paired with a novel test statistic to decide when the estimate is accurate enough. We prove that this Fisher-tracking strategy achieves optimal performance in both fixed-confidence and fixed-budget regimes, which are commonly invested in the best-arm identification literature. Our analysis overcomes a key technical challenge in the fixed-budget setting -- handling the dependence between the evolving estimate and the query distribution -- by exploiting a structural symmetry in the model and combining large deviation tools with Ville's inequality. Our results provide rigorous theoretical support for simple and efficient adaptive testing procedures.