Predict+Optimize is a recently proposed framework which combines machine learning and constrained optimization, tackling optimization problems that contain parameters that are unknown at solving time. The goal is to predict the unknown parameters and use the estimates to solve for an estimated optimal solution to the optimization problem. However, all prior works have focused on the case where unknown parameters appear only in the optimization objective and not the constraints, for the simple reason that if the constraints were not known exactly, the estimated optimal solution might not even be feasible under the true parameters. The contributions of this paper are two-fold. First, we propose a novel and practically relevant framework for the Predict+Optimize setting, but with unknown parameters in both the objective and the constraints. We introduce the notion of a correction function, and an additional penalty term in the loss function, modelling practical scenarios where an estimated optimal solution can be modified into a feasible solution after the true parameters are revealed, but at an additional cost. Second, we propose a corresponding algorithmic approach for our framework, which handles all packing and covering linear programs. Our approach is inspired by the prior work of Mandi and Guns, though with crucial modifications and re-derivations for our very different setting. Experimentation demonstrates the superior empirical performance of our method over classical approaches.

本文提出了一个新的Predict+Optimize框架，可以处理既有在优化目标又有在约束条件中的未知参数，引入了校正函数和惩罚项来解决相关问题，同时提出了一种可处理所有packing和covering线性方程的算法，实验证明该方法比传统方法表现优秀。

在约束条件未知的情况下，预测并优化装箱和覆盖线性规划问题