Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees
This work addresses the problem of ensuring feasible solutions in optimization with data-driven constraints for researchers and practitioners, offering a principled approach with statistical guarantees, though it appears incremental as it builds on existing constraint learning methods.
The paper tackles the problem of data-driven constraints in optimization often violating true constraints due to model error, by proposing Conformal Mixed-Integer Constraint Learning (C-MICL) to provide probabilistic feasibility guarantees, achieving target feasibility rates and reducing computational cost in experiments.
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 $1{-}α$, 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.