Risk-Controlled Selective LLM Answering by Pricing Label-Free Checks

Abstract:Serving an answer from a large language model requires deciding when to abstain, yet a verifier's ranking accuracy alone does not determine the error rate among served answers. We introduce PriceCheck, which builds a compact family of decision rules from label-free checks such as re-solving a problem. Each check has a price: its agreement rates on correct and incorrect answers and its cost per run. Prices fitted on a small, class-enriched labelled set compose into predictions of a schedule's coverage and cost, guiding which checks to run and when to stop. A calibration test then selects a schedule at a stated selective-risk target. In mathematics, the selected schedules serve 76.1% of answers on average and keep held-out selective risk below 1.5% on all 15 splits. Under the shared testing protocol, PriceCheck serves more answers at that target than reward models, a prompted judge, the generator's confidence and a trained correctness classifier. At matched coverage, it keeps the fewest wrong answers among these scorers. Across 118 diagnostic schedules, price-based coverage predictions have a rank correlation of 0.97 with observed coverage. These results show that choosing how checks are combined and stopped matters alongside how well a verifier ranks answers. Code is available at this https URL.

29 pages, 6 figures, 24 tables. Dongyub Jude Lee and Jungseob Lee contributed equally

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)

arXiv:2609.37493 [cs.LG]

(or arXiv:2609.37493v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.37493 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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