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

TL;DR

This paper introduces a unified ensemble learning framework for inverse linear optimization, enabling better model fitting and evaluation, and demonstrates its effectiveness in improving radiation therapy treatment planning.

Contribution

It unifies various inverse optimization models into a single framework, providing exact solution methods and extending goodness-of-fit metrics to ensemble settings.

Findings

The framework accurately fits cost vectors from multiple decisions.

It improves treatment plan quality in radiation therapy.

The consensus approach outperforms baseline methods.

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.