中国科学院数学与系统科学研究院

科研进展与学术交流报告会

（第98期）

报告人：邹长亮 教授（南开大学）

题  目：Adaptive Conformal Uncertainty Sets for Contextual Robust Optimization: A Data-Driven Selection Framework

摘  要：Contextual robust optimization enhances decision-making under uncertainty by incorporating covariate-dependent information to safeguard against the variability of uncertain parameters. Recent work leverages conformal inference to build statistically valid uncertainty sets for machine learning models; however, the downstream optimization performance is highly sensitive to the design of these sets—a critical factor frequently neglected in practice. We propose a novel framework that dynamically adapts conformal uncertainty sets to both the observed covariates and the structure of the downstream optimization problem. By bridging conformal prediction with decision-aware robust optimization, our method automatically tailors uncertainty sets to the problem context, achieving an optimal trade-off between robustness and conservativeness without violating pre-specified probabilistic guarantees. Theoretically, we prove that the framework achieves finite-sample coverage guarantees and near-optimality in solution quality. Numerical experiments across diverse applications show significant improvements in cost efficiency and constraint satisfaction compared to non-contextual approaches. By bridging statistical learning with decision-aware optimization, this work offers a principled data-driven paradigm for adaptive uncertainty quantification in real-world systems.

时  间：2025.3.7(星期五), 10:40-11:50

地  点：南楼204会议室，腾讯会议地址：907-5908-5643