Selected-Risk Calibration for Feasibility at Returned Decisions
Abstract
When an optimization problem uses a surrogate constraint, a decision that is feasible for the surrogate need not be feasible for the true constraint. We propose Selected-Risk Calibration (SRC), a framework that calibrates a learned constraint against the optimizer's returned decisions for objectives drawn from a given distribution. SRC guarantees that, with probability at least 1−δ, every margin it certifies on held-out objectives has selected risk, the probability that the returned decision is infeasible, of at most γ. We also show that the random-input coverage guarantee of split conformal prediction does not bound the selected risk, and that likelihood-ratio reweighting for feedback covariate shift does not apply when the learned constraint is active at the returned decision. Our experiments show that a conformal margin covering about 90% of random inputs covered as few as 17% of the returned decisions, and every certified margin had a violation rate below its target on unseen objectives. Moreover, at equal cost, SRC's correction had fewer or equal infeasible solutions to the baselines in 57 of 62 comparisons. The SRC framework applies to any setting in which a surrogate model chooses a decision whose feasibility can be verified for a sample of instances.
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BibTeX
@misc{thind2026selectedrisk,
title = {{Selected-Risk Calibration for Feasibility at Returned Decisions}},
author = {Raghav Thind and Youran Sun and Ling Liang and Haizhao Yang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.10050},
eprint = {2611.10050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.10050},
}
RIS
TY - UNPB
TI - Selected-Risk Calibration for Feasibility at Returned Decisions
AU - Raghav Thind
AU - Youran Sun
AU - Ling Liang
AU - Haizhao Yang
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.10050
UR - https://arxiv.org/abs/2611.10050
AB - When an optimization problem uses a surrogate constraint, a decision that is feasible for the surrogate need not be feasible for the true constraint. We propose Selected-Risk Calibration (SRC), a framework that calibrates a learned constraint against the optimizer's returned decisions for objectives drawn from a given distribution. SRC guarantees that, with probability at least 1−δ, every margin it certifies on held-out objectives has selected risk, the probability that the returned decision is infeasible, of at most γ. We also show that the random-input coverage guarantee of split conformal prediction does not bound the selected risk, and that likelihood-ratio reweighting for feedback covariate shift does not apply when the learned constraint is active at the returned decision. Our experiments show that a conformal margin covering about 90% of random inputs covered as few as 17% of the returned decisions, and every certified margin had a violation rate below its target on unseen objectives. Moreover, at equal cost, SRC's correction had fewer or equal infeasible solutions to the baselines in 57 of 62 comparisons. The SRC framework applies to any setting in which a surrogate model chooses a decision whose feasibility can be verified for a sample of instances.
ER -