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.

翻译：许多人工智能与运筹学中的决策过程被建模为参数优化问题，其定义参数未知且需从可观测数据中推断。机器学习中的"预测-然后-优化"(PtO)范式旨在通过将参数推理模型与后续带约束优化进行端到端训练，最大化下游决策质量。这要求针对优化问题的特定形式（尤其是不可微的线性与混合整数规划）使用近似技术，通过优化问题实现反向传播。本文将PtO方法体系扩展至具有不可微有序加权平均(OWA)目标的优化问题——该目标函数因其在决策模型中确保公平性与鲁棒性的能力而著称。通过一系列训练技术与所提出的应用场景，本文展示了如何将OWA函数的优化与参数预测有效集成，以实现在不确定性条件下的公平与鲁棒优化。