An Extended Validity Domain for Constraint Learning

Information Systems and Operations Management 

Speaker: Samuel Burer (U Iowa Tippie)

Room Bernard Ramanantsoa

Abstract

We consider embedding a (predictive) machine-learning model within a (prescriptive) optimization problem. In this setting, called constraint learning, the computed optimal solution may be too far from the training data, that is, in a region where the machine-learning predictions are less accurate. To correct for this, researchers have proposed the concept of a validity domain, which further constrains the optimization to stay close to the training data. One common choice forces the decision variable to lie within the convex hull of the data. In this talk, we propose a new validity domain, which uses the convex-hull idea in an extended space. We investigate its properties and compare it empirically with existing techniques on a set of test problems for which the ground-truth optimization problem is known. We also consider our approach within a pricing case study using real-world data. This is joint work with Yilin Zhu at the University of Iowa.