Constraint Learning to Define Trust Regions in Predictive-Model Embedded Optimization

Abstract

There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is predictive-model embedded optimization, which uses pre-trained predictive models for the objective function of an optimization problem, so that features of the predictive models become decision variables in the optimization problem. Despite a recent surge in publications in this area, one aspect of this decision-making pipeline that has been largely overlooked is training relevance, i.e., ensuring that solutions to the optimization problem should be similar to the data used to train the predictive models. In this paper, we propose constraints designed to enforce training relevance, and show through a collection of experimental results that adding the suggested constraints significantly improves the quality of solutions obtained.