Speaker: 邹长亮教授，南开大学

Inviter: 中国科学院数学院学术报告会组委

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

Language: Chinese

Time & Venue: 2025.03.07 10:40-11:50 数学院南楼N204（数学院交流报告会）

Abstract: 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.