On the Optimality of Tracking Fisher Information in Adaptive Testing with Stochastic Binary Responses
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916998336741376 |
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| author | Kim, Sanghwa Ahn, Dohyun Min, Seungki |
| author_facet | Kim, Sanghwa Ahn, Dohyun Min, Seungki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07862 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Optimality of Tracking Fisher Information in Adaptive Testing with Stochastic Binary Responses Kim, Sanghwa Ahn, Dohyun Min, Seungki Machine Learning 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. |
| title | On the Optimality of Tracking Fisher Information in Adaptive Testing with Stochastic Binary Responses |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.07862 |