Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees

2025-06-04

AI Summary

In data-driven optimization, model inaccuracies or insufficient training data often lead to constraint violations and infeasible solutions. Method: This paper introduces conformal prediction into a mixed-integer constrained learning framework for the first time, enabling probabilistic feasibility guarantees (≥1−α) for optimization solutions without requiring access to the true constraint functions. The approach integrates conformal prediction, mixed-integer programming, and regression/classification modeling—replacing inefficient heuristic ensembles with a statistically principled, unified methodology. Contribution/Results: Theoretical analysis ensures statistical validity under mild assumptions, while algorithmic design emphasizes scalability. Experiments on real-world benchmarks demonstrate that the method consistently achieves the target feasibility rate, attains objective performance comparable to state-of-the-art methods, and significantly reduces computational overhead.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Ensures probabilistic feasibility guarantees for data-driven constraints
• Avoids violating true constraints due to model errors
• Reduces computational cost while maintaining feasibility rates

Innovation

• Conformal prediction ensures probabilistic feasibility guarantees
• Supports regression and classification without true constraints
• Reduces computational cost while maintaining feasibility rates