A Unified Framework for Model Fitting and Evaluation in Inverse Linear Optimization

We develop a generalized inverse optimization framework for fitting the cost vector of a single linear optimization problem given an ensemble of observed decisions. We unify multiple variants in the inverse optimization literature under a common template and derive assumption-free and exact solution methods for each variant. We extend a goodness-of-fit metric previously introduced for the problem with a single observed decision to this new setting, proving and numerically demonstrating several important properties. Finally, to illustrate our framework, we develop a novel inverse optimization-driven procedure for automated radiation therapy treatment planning. Here, the inverse optimization model leverages the combined power of an ensemble of dose predictions produced by different machine learning models to construct clinical treatment plans that better trade off between the competing clinical objectives that are used for plan evaluation in practice.