LEC: Linear Expectation Constraints for Selection-Conditioned Risk Control in Selective Prediction and Routing Systems

Fuente: arXiv
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Main Authors: Wang, Zhiyuan, Aniri, Chen, Tianlong, Zhang, Yue, Shen, Heng Tao, Shi, Xiaoshuang, Xu, Kaidi
Format: Preprint
Published: 2025
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author Wang, Zhiyuan
Aniri
Chen, Tianlong
Zhang, Yue
Shen, Heng Tao
Shi, Xiaoshuang
Xu, Kaidi
author_facet Wang, Zhiyuan
Aniri
Chen, Tianlong
Zhang, Yue
Shen, Heng Tao
Shi, Xiaoshuang
Xu, Kaidi
contents Foundation models often generate unreliable answers, while heuristic uncertainty estimators fail to fully distinguish correct from incorrect outputs, causing users to accept erroneous answers without any statistical guarantee. We address this problem through selection-conditioned risk control, aiming to ensure that an accepted prediction has an error probability no larger than a user-specified risk level. To this end, we propose LEC, a principled framework that reframes selective prediction as a decision problem governed by a linear expectation constraint over selection and error indicators. This formulation directly controls the ratio between the expected number of accepted errors and the expected number of accepted predictions, which corresponds to the marginal error probability conditioned on selection. Under exchangeability, we derive a finite-sample sufficient condition that relies only on a held-out calibration set, enabling the computation of a risk-constrained, retention-maximizing threshold. Furthermore, we extend LEC to two-model routing systems: if the primary model's uncertainty exceeds its calibrated threshold, the input is delegated to a subsequent model, while maintaining system-level selection-conditioned error control. Experiments on both closed-ended and open-ended question answering (QA) and vision question answering (VQA) demonstrate that LEC maintains the prescribed risk level in accepted predictions and substantially improves sample retention compared to baselines.
format Preprint
id arxiv_https___arxiv_org_abs_2512_01556
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle LEC: Linear Expectation Constraints for Selection-Conditioned Risk Control in Selective Prediction and Routing Systems
Wang, Zhiyuan
Aniri
Chen, Tianlong
Zhang, Yue
Shen, Heng Tao
Shi, Xiaoshuang
Xu, Kaidi
Artificial Intelligence
Computation and Language
Machine Learning
Foundation models often generate unreliable answers, while heuristic uncertainty estimators fail to fully distinguish correct from incorrect outputs, causing users to accept erroneous answers without any statistical guarantee. We address this problem through selection-conditioned risk control, aiming to ensure that an accepted prediction has an error probability no larger than a user-specified risk level. To this end, we propose LEC, a principled framework that reframes selective prediction as a decision problem governed by a linear expectation constraint over selection and error indicators. This formulation directly controls the ratio between the expected number of accepted errors and the expected number of accepted predictions, which corresponds to the marginal error probability conditioned on selection. Under exchangeability, we derive a finite-sample sufficient condition that relies only on a held-out calibration set, enabling the computation of a risk-constrained, retention-maximizing threshold. Furthermore, we extend LEC to two-model routing systems: if the primary model's uncertainty exceeds its calibrated threshold, the input is delegated to a subsequent model, while maintaining system-level selection-conditioned error control. Experiments on both closed-ended and open-ended question answering (QA) and vision question answering (VQA) demonstrate that LEC maintains the prescribed risk level in accepted predictions and substantially improves sample retention compared to baselines.
title LEC: Linear Expectation Constraints for Selection-Conditioned Risk Control in Selective Prediction and Routing Systems
topic Artificial Intelligence
Computation and Language
Machine Learning
url https://arxiv.org/abs/2512.01556