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.

通过训练技术和应用设置，本文将 PtO 方法扩展到具有不可微分的有序加权平均目标的优化问题，展示了如何在不确定性下有效地将 OWA 函数优化与参数预测相结合，以实现公平和稳健的优化。

不确定性下公平多目标优化的端到端学习

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

This paper presents Dual Lagrangian Learning (DLL), a principled learning
methodology that combines conic duality theory with the represen- tation power
of ML models. DLL leverages conic duality to provide dual-feasible solutions,
and therefore valid Lagrangian dual bounds, for para- metric linear and
nonlinear conic optimization problems. The paper introduces differentiable
conic projection layers, a systematic dual com- pletion procedure, and a
self-supervised learning framework. The effectiveness of DLL is demon- strated
on linear and nonlinear parametric opti- mization problems for which DLL
provides valid dual bounds within 0.5% of optimality.

该研究论文介绍了双拉格朗日学习 (DLL) 方法，该方法将锥对偶理论与机器学习模型的表示能力相结合。DLL 利用锥对偶性提供对偶可行解，从而为参数线性和非线性锥优化问题提供有效的拉格朗日对偶界限。该论文介绍了可微锥投影层、系统性的对偶完成过程和自监督学习框架。DLL 的有效性已在线性和非线性参数优化问题上得到证明，其中 DLL 提供的有效对偶界限与最优解相差不超过 0.5%。