In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters $w$ are not directly observed; only contextual data $d$ that correlates with $w$ is available. It is tempting to use a neural network to predict $w$ given $d$, but training such a model requires reconciling the discrete nature of combinatorial optimization with the gradient-based frameworks used to train neural networks. When the problem in question is an Integer Linear Program (ILP), one approach to overcoming this issue is to consider a continuous relaxation of the combinatorial problem. While existing methods utilizing this approach have shown to be highly effective on small problems (10-100 variables), they do not scale well to large problems. In this work, we draw on ideas from modern convex optimization to design a network and training scheme which scales effortlessly to problems with thousands of variables.

翻译：在许多应用中，需要反复求解参数相似但略有不同的组合优化问题。然而，参数$w$无法直接观测，仅能获得与$w$相关的上下文数据$d$。一种直观方法是利用神经网络根据$d$预测$w$，但训练此类模型需要协调组合优化的离散特性与神经网络训练中基于梯度的框架。当待求解问题为整数线性规划（ILP）时，克服这一难题的途径之一是考虑组合问题的连续松弛。尽管现有采用该方法的模型在小型问题（10-100个变量）上效果显著，但难以扩展至大规模问题。本研究借鉴现代凸优化思想，设计了一种网络结构与训练方案，可轻松扩展至包含数千个变量的问题。