We address the problem of prescribing an optimal decision in a framework where the cost function depends on uncertain problem parameters that need to be learned from data. Earlier work proposed prescriptive formulations based on supervised machine learning methods. These prescriptive methods can factor in contextual information on a potentially large number of covariates to take context specific actions which are superior to any static decision. When working with noisy or corrupt data, however, such nominal prescriptive methods can be prone to adverse overfitting phenomena and fail to generalize on out-of-sample data. In this paper we combine ideas from robust optimization and the statistical bootstrap to propose novel prescriptive methods which safeguard against overfitting. We show indeed that a particular entropic robust counterpart to such nominal formulations guarantees good performance on synthetic bootstrap data. As bootstrap data is often a sensible proxy to actual out-of-sample data, our robust counterpart can be interpreted to directly encourage good out-of-sample performance. The associated robust prescriptive methods furthermore reduce to convenient tractable convex optimization problems in the context of local learning methods such as nearest neighbors and Nadaraya–Watson learning. We illustrate our data-driven decision-making framework and our novel robustness notion on a small newsvendor problem.

我们解决了在成本函数取决于需要从数据中学习的不确定问题参数的框架中制定最佳决策的问题。早期的工作提出了基于监督机器学习方法的规范公式。这些规定性方法可以将有关潜在大量协变量的上下文信息考虑在内，以采取优于任何静态决策的上下文特定操作。然而，在处理嘈杂或损坏的数据时，这种名义上的规范方法可能容易出现不利的过度拟合现象，并且无法对样本外数据进行泛化。在本文中，我们结合了稳健优化和统计引导程序的思想，提出了防止过度拟合的新规范方法。我们确实表明，这种名义公式的特定熵鲁棒对应物保证了合成引导数据的良好性能。由于引导数据通常是实际样本外数据的合理代理，因此我们的稳健对应物可以被解释为直接鼓励良好的样本外表现。在本地学习方法（例如最近邻和 Nadaraya-Watson 学习）的背景下，相关联的稳健规范方法进一步简化为方便易处理的凸优化问题。我们说明了我们的数据驱动决策框架和我们对小型报摊问题的新颖稳健性概念。我们稳健的对应物可以被解释为直接鼓励良好的样本外表现。在本地学习方法（例如最近邻和 Nadaraya-Watson 学习）的背景下，相关联的稳健规范方法进一步简化为方便易处理的凸优化问题。我们说明了我们的数据驱动决策框架和我们对小型报摊问题的新颖稳健性概念。我们稳健的对应物可以被解释为直接鼓励良好的样本外表现。在本地学习方法（例如最近邻和 Nadaraya-Watson 学习）的背景下，相关联的稳健规范方法进一步简化为方便易处理的凸优化问题。我们说明了我们的数据驱动决策框架和我们对小型报摊问题的新颖稳健性概念。