Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees

• URL: http://arxiv.org/abs/2506.03531v1
• Date: Wed, 04 Jun 2025 03:26:31 GMT
• Title: Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees
• Authors: Daniel Ovalle, Lorenz T. Biegler, Ignacio E. Grossmann, Carl D. Laird, Mateo Dulce Rubio,
• Abstract summary: Conformal Mixed-Integer Constraint Learning provides probabilistic feasibility guarantees for data-driven constraints in optimization problems.<n>We show that C-MICL consistently achieves target rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods.
• Score: 0.3058340744328236
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning methods often violate the true constraints due to model error or data limitations, our C-MICL approach leverages conformal prediction to ensure feasible solutions are ground-truth feasible. This guarantee holds with probability at least $1{-}\alpha$, under a conditional independence assumption. The proposed framework supports both regression and classification tasks without requiring access to the true constraint function, while avoiding the scalability issues associated with ensemble-based heuristics. Experiments on real-world applications demonstrate that C-MICL consistently achieves target feasibility rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods. Our work bridges mathematical optimization and machine learning, offering a principled approach to incorporate uncertainty-aware constraints into decision-making with rigorous statistical guarantees.

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