Consider the setting of constrained optimization, with some parameters unknown at solving time and requiring prediction from relevant features. Predict+Optimize is a recent framework for end-to-end training supervised learning models for such predictions, incorporating information about the optimization problem in the training process in order to yield better predictions in terms of the quality of the predicted solution under the true parameters. Almost all prior works have focused on the special case where the unknowns appear only in the optimization objective and not the constraints. Hu et al.~proposed the first adaptation of Predict+Optimize to handle unknowns appearing in constraints, but the framework has somewhat ad-hoc elements, and they provided a training algorithm only for covering and packing linear programs. In this work, we give a new \emph{simpler} and \emph{more powerful} framework called \emph{Two-Stage Predict+Optimize}, which we believe should be the canonical framework for the Predict+Optimize setting. We also give a training algorithm usable for all mixed integer linear programs, vastly generalizing the applicability of the framework. Experimental results demonstrate the superior prediction performance of our training framework over all classical and state-of-the-art methods.

翻译：考虑约束优化场景，部分参数在求解时未知，需根据相关特征进行预测。“预测+优化”是一种近期提出的端到端训练监督学习模型框架，旨在通过将优化问题信息融入训练过程，提升基于真实参数预测解的质量。现有研究几乎均聚焦于未知参数仅出现在优化目标中而不含约束的特殊情形。Hu等人首次提出将“预测+优化”框架扩展至约束含未知参数的情况，但其框架存在临时性设计缺陷，且仅针对覆盖与打包线性规划问题设计了训练算法。本文提出一个更简洁且更强大的新框架——两阶段预测+优化，该框架应成为“预测+优化”场景的标准范式。同时，我们给出了适用于所有混合整数线性规划的训练算法，极大拓展了框架的适用性。实验结果表明，相较于所有经典及最新方法，本训练框架在预测性能上具有显著优势。