The Good, the Bad, and the Sampled: a No-Regret Approach to Safe Online Classification
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910184230617088 |
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| author | Baharav, Tavor Z. Dragazis, Spyros Pacchiano, Aldo |
| author_facet | Baharav, Tavor Z. Dragazis, Spyros Pacchiano, Aldo |
| contents | We study sequential testing for a binary disease outcome when risk follows an unknown logistic model. At each round, the decision maker may either pay for a test revealing the true label or predict the outcome based on patient features and past data. The goal is to minimize costly tests while ensuring the misclassification rate stays below $α$ with probability at least $1-δ$. We propose a method that jointly estimates the logistic parameter $θ^{\star}$ and the feature distribution, using a conservative threshold on the logistic score to decide when to test. We prove our procedure achieves the target error with high probability and requires only $\widetilde O(\sqrt{T})$ more tests than an oracle with full knowledge. This is the first no-regret guarantee for error-constrained logistic testing, with direct applications to medical screening. Simulations corroborate our theoretical results, showing safe classification of patients and efficient estimation of $θ^{\star}$ with few excess tests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Good, the Bad, and the Sampled: a No-Regret Approach to Safe Online Classification Baharav, Tavor Z. Dragazis, Spyros Pacchiano, Aldo Machine Learning Artificial Intelligence Statistics Theory We study sequential testing for a binary disease outcome when risk follows an unknown logistic model. At each round, the decision maker may either pay for a test revealing the true label or predict the outcome based on patient features and past data. The goal is to minimize costly tests while ensuring the misclassification rate stays below $α$ with probability at least $1-δ$. We propose a method that jointly estimates the logistic parameter $θ^{\star}$ and the feature distribution, using a conservative threshold on the logistic score to decide when to test. We prove our procedure achieves the target error with high probability and requires only $\widetilde O(\sqrt{T})$ more tests than an oracle with full knowledge. This is the first no-regret guarantee for error-constrained logistic testing, with direct applications to medical screening. Simulations corroborate our theoretical results, showing safe classification of patients and efficient estimation of $θ^{\star}$ with few excess tests. |
| title | The Good, the Bad, and the Sampled: a No-Regret Approach to Safe Online Classification |
| topic | Machine Learning Artificial Intelligence Statistics Theory |
| url | https://arxiv.org/abs/2510.01020 |