An Ensemble Learning Framework for Model Fitting and Evaluation in Inverse Linear Optimization

Abstract

We develop a generalized inverse optimization framework for fitting the cost vector of a single linear optimization problem given multiple observed decisions. This setting is motivated by ensemble learning, where building consensus from base learners can yield better predictions. We unify several models in the inverse optimization literature under a single framework and derive assumption-free and exact solution methods for each one. We extend a goodness-of-fit metric previously introduced for the problem with a single observed decision to this new setting and demonstrate several important properties. Finally, we demonstrate our framework in a novel inverse optimization-driven procedure for automated radiation therapy treatment planning. Here, the inverse optimization model leverages an ensemble of dose predictions from different machine learning models to construct a consensus treatment plan that outperforms baseline methods. The consensus plan yields better trade-offs between the competing clinical criteria used for plan evaluation.