Training neural network surrogates with MILP-aware regularizers can dramatically speed up downstream optimization without sacrificing accuracy, by directly controlling structural properties that affect solver performance.
This paper shows how to train neural networks as surrogate models that work better when embedded in optimization problems. By adding special regularizers during training that target MILP tractability—penalizing large constants, unstable neurons, and LP relaxation gaps—the approach makes the resulting optimization problems solve 10,000x faster while keeping prediction accuracy competitive.