Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Ovalle, Daniel Biegler, Lorenz T. Grossmann, Ignacio E. Laird, Carl D. Rubio, Mateo Dulce |
| author_facet | Ovalle, Daniel Biegler, Lorenz T. Grossmann, Ignacio E. Laird, Carl D. Rubio, Mateo Dulce |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees Ovalle, Daniel Biegler, Lorenz T. Grossmann, Ignacio E. Laird, Carl D. Rubio, Mateo Dulce Machine Learning Optimization and Control 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. |
| title | Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2506.03531 |