Local Violation Certification for Linear Predict-Then-Optimize Pipelines

What the math gives to ML

The paper turns a rare-event safety question into a local geometric calculation: when the deployed decision pipeline is affine in a neighborhood, the violation event is a half-space and its probability under a Gaussian local input model is determined by one Mahalanobis distance. This structure can be transferred to neural networks by linearizing a scalar safety margin, such as a constraint residual or adversarial loss, around each input and estimating the probability of crossing the local boundary without Monte Carlo trials. The useful asset is the combination of a closed-form Gaussian crossing probability, an explicit approximation-error allowance for leaving the locally affine region, and feature-level attribution through the covariance-weighted normal vector. A practical use is an inexpensive local-risk regularizer or abstention certificate for neural predictors.