The abundance of data has led to the emergence of a variety of optimization techniques that attempt to leverage available side information to provide more anticipative decisions. The wide range of methods and contexts of application have motivated the design of a universal unitless measure of performance known as the coefficient of prescriptiveness. This coefficient was designed to quantify both the quality of contextual decisions compared to a reference one and the prescriptive power of side information. To identify policies that maximize the former in a data-driven context, this paper introduces a distributionally robust contextual optimization model where the coefficient of prescriptiveness substitutes for the classical empirical risk minimization objective. We present a bisection algorithm to solve this model, which relies on solving a series of linear programs when the distributional ambiguity set has an appropriate nested form and polyhedral structure. Studying a contextual shortest path problem, we evaluate the robustness of the resulting policies against alternative methods when the out-of-sample dataset is subject to varying amounts of distribution shift.

翻译：数据的丰富性催生了多种优化技术，这些技术试图利用可用的辅助信息来制定更具前瞻性的决策。广泛的方法和应用背景促使设计一种通用的无量纲性能度量——处方性系数。该系数旨在量化相较于参考决策的背景决策质量以及辅助信息的处方能力。为在数据驱动背景下识别最大化前者的策略，本文引入了一种分布鲁棒背景优化模型，其中以处方性系数替代经典的经验风险最小化目标。我们提出了一种二分法算法来求解该模型，当分布模糊集具有适当的嵌套形式和多面体结构时，该算法依赖于求解一系列线性规划问题。通过研究一个背景最短路径问题，我们评估了所得策略在样本外数据集经历不同程度分布偏移时相较于其他方法的鲁棒性。