Sampling from the complement of a polyhedron: An MCMC algorithm for data augmentation

Timothy C. Y. Chan, Adam Diamant, Rafid Mahmood

Abstract: We present an MCMC algorithm for sampling from the complement of a polyhedron. Our approach is based on the Shake-and-bake algorithm for sampling from the boundary of a set and provably covers the complement. We use this algorithm for data augmentation in a machine learning task of classifying a hidden feasible set in a data-driven optimization pipeline. Numerical results on simulated and MIPLIB instances demonstrate that our algorithm, along with a supervised learning technique, outperforms conventional unsupervised baselines.