Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees

TL;DR

This paper introduces C-MICL, a framework that uses conformal prediction to provide probabilistic feasibility guarantees in data-driven mixed-integer constraint learning, ensuring solutions are feasible with high probability.

Contribution

C-MICL is the first method to offer probabilistic feasibility guarantees for mixed-integer constraint learning without requiring access to the true constraint function.

Findings

Achieves target feasibility rates in real-world applications

Maintains competitive objective performance

Reduces computational cost compared to existing methods

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.