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 https://github.com/js-lee-AI/PriceCheck.
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Cite this article
APA 7
Lee, D. J., Lee, J., Park, C., Moon, H., & Lim, H. (2026). Risk-Controlled Selective LLM Answering by Pricing Label-Free Checks. https://omanscience.com/en/articles/risk-controlled-selective-llm-answering-by-pricing-label-free-checks
MLA 9
Lee, Dongyub Jude, et al. "Risk-Controlled Selective LLM Answering by Pricing Label-Free Checks." https://omanscience.com/en/articles/risk-controlled-selective-llm-answering-by-pricing-label-free-checks.
Chicago (author–date)
Lee, Dongyub Jude, Jungseob Lee, Chanjun Park, Hyeonseok Moon, and Heuiseok Lim. 2026. "Risk-Controlled Selective LLM Answering by Pricing Label-Free Checks." https://omanscience.com/en/articles/risk-controlled-selective-llm-answering-by-pricing-label-free-checks.
Harvard
Lee, D. J., Lee, J., Park, C., Moon, H. and Lim, H. (2026) 'Risk-Controlled Selective LLM Answering by Pricing Label-Free Checks', Available at: https://omanscience.com/en/articles/risk-controlled-selective-llm-answering-by-pricing-label-free-checks.
Vancouver
Lee DJ, Lee J, Park C, Moon H, Lim H. Risk-Controlled Selective LLM Answering by Pricing Label-Free Checks. https://omanscience.com/en/articles/risk-controlled-selective-llm-answering-by-pricing-label-free-checks
IEEE
D. J. Lee, J. Lee, C. Park, H. Moon, and H. Lim, "Risk-Controlled Selective LLM Answering by Pricing Label-Free Checks," https://omanscience.com/en/articles/risk-controlled-selective-llm-answering-by-pricing-label-free-checks.