Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find optimal solutions. In this paper we prove the first guarantees for learning high-performing cut-selection policies tailored to the instance distribution at hand using samples. We first bound the sample complexity of learning cutting planes from the canonical family of Chv\'atal-Gomory cuts. Our bounds handle any number of waves of any number of cuts and are fine tuned to the magnitudes of the constraint coefficients. Next, we prove sample complexity bounds for more sophisticated cut selection policies that use a combination of scoring rules to choose from a family of cuts. Finally, beyond the realm of cutting planes for integer programming, we develop a general abstraction of tree search that captures key components such as node selection and variable selection. For this abstraction, we bound the sample complexity of learning a good policy for building the search tree.

翻译：切片方法在过去几十年里使整数编程取得了显著的成功。 最先进的解算器整合了无数的切片技术, 以加快用于寻找最佳解决方案的原始树搜索算法。 在本文中, 我们证明我们学习高性能剪切政策的第一个保障, 这些政策是针对手头使用样本进行分配的。 我们首先将从Chv\'atal- Gomory 裁剪的卡通式家庭学习剪切片的样本复杂性绑定起来。 我们的界限可以处理任何数量的任何波级的切片, 并且能够精确地适应制约系数的大小。 下一步, 我们证明样本的复杂性是更精密的剪切选择政策的界限, 使用评分法的组合来从切片组中做出选择。 最后, 在剪切图的范畴以外, 我们开发了一种一般的树搜索抽象模型, 以捕捉取关键组成部分, 如节选和变量选择 。 对于这个抽象的, 我们把为建立搜索树学习好的政策的样本复杂性绑定了 。