两阶段预测+优化用于约束中参数未知的混合整数线性规划
Two-Stage Predict+Optimize for Mixed Integer Linear Programs with Unknown Parameters in Constraints
AI总结：
本文提出两阶段预测+优化框架，用于处理约束中参数未知的混合整数线性规划，提供通用训练算法，实验显示预测性能优于现有方法。
摘要：
考虑约束优化的设置，其中一些参数在求解时未知，需要从相关特征进行预测。预测+优化（Predict+Optimize）是一个最近的框架，用于此类预测的端到端训练监督学习模型，在训练过程中纳入优化问题的信息，以便在真实参数下根据预测解的质量产生更好的预测。几乎所有先前的工作都集中在未知数仅出现在优化目标中而非约束中的特殊情况。Hu等人提出了第一个适应预测+优化以处理约束中出现未知数的框架，但该框架有一些临时性元素，并且他们仅为覆盖和打包线性规划提供了训练算法。在这项工作中，我们给出了一个新的更简单且更强大的框架，称为两阶段预测+优化（Two-Stage Predict+Optimize），我们认为这应该是预测+优化设置的规范框架。我们还给出了一种适用于所有混合整数线性规划的训练算法，极大地推广了该框架的适用性。实验结果表明，我们的训练框架在预测性能上优于所有经典和最先进的方法。
英文摘要：
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.
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