Occupancy-based Quantile Risk Control
Abstract
Conformal risk control is an emerging framework for the safe deployment of machine learning models with finite-sample guarantees. To accommodate a broader class of risk notions, quantile risk control extends this framework to quantile-based risk measures. However, existing methods either suffer from excessive conservatism or lack rigorous finite-sample guarantees. To address these limitations, we introduce Occupancy-based Quantile Risk Control (OQRC), a novel method that provides tight risk control bounds with finite-sample validity. Our key idea is to formulate risk control as a finite-occupancy problem by partitioning the loss space with the ordered calibration losses. Specifically, we estimate the distribution of test losses across the resulting bins and upper-bound the risk by the maximum loss attained within each bin. We then select the parameter λ such that this upper bound does not exceed a predefined threshold α with high probability 1−δ. Theoretically, we establish a finite-sample guarantee showing that OQRC yields tight risk control bounds that converge to the optimal bounds at a provable rate of 𝒪p(n−1/2). Extensive experiments demonstrate the effectiveness of our method, reducing the risk gap by up to 78.64\% on common benchmarks.
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BibTeX
@misc{shi2026occupancybased,
title = {{Occupancy-based Quantile Risk Control}},
author = {Zihao Shi and Huajun Xi and Bingyi Jing and Hongxin Wei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03104},
eprint = {2609.03104},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03104},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Occupancy-based Quantile Risk Control
AU - Zihao Shi
AU - Huajun Xi
AU - Bingyi Jing
AU - Hongxin Wei
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03104
UR - https://arxiv.org/abs/2609.03104
AB - Conformal risk control is an emerging framework for the safe deployment of machine learning models with finite-sample guarantees. To accommodate a broader class of risk notions, quantile risk control extends this framework to quantile-based risk measures. However, existing methods either suffer from excessive conservatism or lack rigorous finite-sample guarantees. To address these limitations, we introduce Occupancy-based Quantile Risk Control (OQRC), a novel method that provides tight risk control bounds with finite-sample validity. Our key idea is to formulate risk control as a finite-occupancy problem by partitioning the loss space with the ordered calibration losses. Specifically, we estimate the distribution of test losses across the resulting bins and upper-bound the risk by the maximum loss attained within each bin. We then select the parameter λ such that this upper bound does not exceed a predefined threshold α with high probability 1−δ. Theoretically, we establish a finite-sample guarantee showing that OQRC yields tight risk control bounds that converge to the optimal bounds at a provable rate of 𝒪_p(n^−1/2). Extensive experiments demonstrate the effectiveness of our method, reducing the risk gap by up to 78.64\% on common benchmarks.
ER -