CG4AI Trains AI Models with Guaranteed Output Constraints

Traditional machine learning model training primarily focuses on minimizing a loss function, often without explicitly guaranteeing that the model's outputs will adhere to specific predefined rules or constraints. In many critical real-world applications, such as autonomous vehicles or network routing, these guarantees are absolutely essential for safety and reliability.This paper introduces CG4AI, a novel framework designed to train AI models while strictly enforcing linear constraints on their combined output. CG4AI operates by constructing a convex combination of multiple AI models. A master linear program determines the optimal weights for this combination, while a pricing subproblem dynamically generates new models, specifically targeting and addressing the most violated constraints.The framework also incorporates a cutting-plane procedure to extend feasibility guarantees beyond the initial training set. Experiments on digit classification (MNIST) demonstrated CG4AI's ability to learn from constraints alone, improve adversarial robustness, correct misclassified examples, and enforce output relabeling. Applied to the multi-commodity flow problem, it successfully enforced link capacity constraints on neural-network routing predictors. Results show CG4AI consistently produces feasible predictors with better accuracy than single-model baselines.