Conformalized Safe Feasible Sets in Uncertain Decision Systems
Abstract
Safety-critical decision systems often require a downstream optimizer to choose from an unknown feasible set determined by an unobserved label Y. Given a context X, the goal is to construct a safe subset D(X) contained in the oracle feasible set A(X,Y) with probability at least 1−α. Existing conformal approaches typically construct a prediction set of the unobserved label Y and retain decisions that are safe for every value in this set. Although valid, this requires a stronger intermediate event than set inclusion. We propose Directed Inclusion Safety Calibration (DISC), a conformal framework that directly controls the probability of this inclusion event by reducing its verification to a scalar critical-inclusion score. Given a pretrained nested family of candidate feasible sets, DISC assigns each labeled observation the smallest nestedness level at which the corresponding subset is contained in A(X,Y), and constructs the safe feasible set using an empirical quantile at test-time. With data exchangeability, this yields a finite-sample, distribution-free inclusion guarantee. Under two practical set families, we show that DISC produces a safe feasible set containing that obtained by the corresponding calibration baseline. We further develop optimization-based score computation and decision-aware procedures for learning subset families. Experiments across continuous and structured decision problems show that DISC achieves the target inclusion guarantee while producing larger feasible regions.
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BibTeX
@misc{bao2026conformalized,
title = {{Conformalized Safe Feasible Sets in Uncertain Decision Systems}},
author = {Yajie Bao and Yinjie Min and Haojie Ren and Changliang Zou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24496},
eprint = {2609.24496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24496},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Conformalized Safe Feasible Sets in Uncertain Decision Systems
AU - Yajie Bao
AU - Yinjie Min
AU - Haojie Ren
AU - Changliang Zou
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24496
UR - https://arxiv.org/abs/2609.24496
AB - Safety-critical decision systems often require a downstream optimizer to choose from an unknown feasible set determined by an unobserved label Y. Given a context X, the goal is to construct a safe subset D(X) contained in the oracle feasible set A(X,Y) with probability at least 1−α. Existing conformal approaches typically construct a prediction set of the unobserved label Y and retain decisions that are safe for every value in this set. Although valid, this requires a stronger intermediate event than set inclusion. We propose Directed Inclusion Safety Calibration (DISC), a conformal framework that directly controls the probability of this inclusion event by reducing its verification to a scalar critical-inclusion score. Given a pretrained nested family of candidate feasible sets, DISC assigns each labeled observation the smallest nestedness level at which the corresponding subset is contained in A(X,Y), and constructs the safe feasible set using an empirical quantile at test-time. With data exchangeability, this yields a finite-sample, distribution-free inclusion guarantee. Under two practical set families, we show that DISC produces a safe feasible set containing that obtained by the corresponding calibration baseline. We further develop optimization-based score computation and decision-aware procedures for learning subset families. Experiments across continuous and structured decision problems show that DISC achieves the target inclusion guarantee while producing larger feasible regions.
ER -