End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty

TL;DR

This paper extends the Predict-Then-Optimize framework to handle nondifferentiable Ordered Weighted Averaging objectives, enabling fair and robust decision-making in uncertain environments through end-to-end learning.

Contribution

It introduces new training techniques for integrating OWA objectives into end-to-end learning, addressing nondifferentiability for fair and robust optimization.

Findings

Effective integration of OWA functions with parametric prediction.

Enhanced fairness and robustness in decision models.

Demonstrated success in application settings.

Abstract

Many decision processes in artificial intelligence and operations research are modeled by parametric optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize (PtO) paradigm in machine learning aims to maximize downstream decision quality by training the parametric inference model end-to-end with the subsequent constrained optimization. This requires backpropagation through the optimization problem using approximation techniques specific to the problem's form, especially for nondifferentiable linear and mixed-integer programs. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives, known for their ability to ensure properties of fairness and robustness in decision models. Through a collection of training techniques and proposed application settings, it shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.