Generalization guarantees for learned MILP models

Establish theoretical generalization results for machine-learning models trained on mixed-integer linear programming (MILP) datasets—such as graph neural networks used for solution prediction or solver guidance—showing that parameters θ* found by minimizing a training objective on one dataset extend to an independent dataset and quantifying the generalization error between training and test performance.

Background

In applying machine learning to MILP—e.g., for learning heuristics, branching rules, cut selection, and instance-specific configuration—models are trained on datasets of problem instances. Despite strong empirical performance, theoretical guarantees that trained models generalize to unseen instances are crucial for robust deployment and understanding.

The authors emphasize that, to the best of their knowledge, rigorous generalization theorems for these learned MILP models are currently lacking, even though generalization is commonly assessed experimentally. Formal bounds would validate that training-time performance carries over to independent test sets.