论文标题
使用无监督的深度学习，数据驱动的强大优化
Data-Driven Robust Optimization using Unsupervised Deep Learning
论文作者
论文摘要
已建立了强大的优化，作为在不确定性下解决决策问题的主要方法。为了得出可靠的优化模型，中央成分是确定适合不确定性的模型，这称为不确定性集。最近的文献中的一个持续挑战是从给定的历史数据中得出不确定性集，这些数据导致解决方案在未来的情况下具有牢固的解决方案。在本文中，我们使用一种无监督的深度学习方法来从数据中学习和提取隐藏的结构，从而导致不确定性集合和更好的健壮解决方案。我们证明，大多数经典不确定性类都是我们派生的集合的特殊情况，并且对它们进行优化是NP坚强的。然而，我们表明，通过将对抗性问题制定为凸二次混合组合程序，可以将受过训练的神经网络集成到强大的优化模型中。这使我们能够通过迭代场景生成过程得出强大的解决方案。在我们的计算实验中，我们将这种方法与基于内核的支持向量聚类的类似方法进行了比较。我们发现，由无监督的深度学习方法得出的不确定性集找到了对数据的更好描述，并导致了强大的解决方案，从而超过了相对于客观价值和可行性的比较方法。
Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called the uncertainty set. An ongoing challenge in the recent literature is to derive uncertainty sets from given historical data that result in solutions that are robust regarding future scenarios. In this paper we use an unsupervised deep learning method to learn and extract hidden structures from data, leading to non-convex uncertainty sets and better robust solutions. We prove that most of the classical uncertainty classes are special cases of our derived sets and that optimizing over them is strongly NP-hard. Nevertheless, we show that the trained neural networks can be integrated into a robust optimization model by formulating the adversarial problem as a convex quadratic mixed-integer program. This allows us to derive robust solutions through an iterative scenario generation process. In our computational experiments, we compare this approach to a similar approach using kernel-based support vector clustering. We find that uncertainty sets derived by the unsupervised deep learning method find a better description of data and lead to robust solutions that outperform the comparison method both with respect to objective value and feasibility.
