We present a novel framework for distributionally robust optimization (DRO), called cost-aware DRO (CADRO). The key idea of CADRO is to exploit the cost structure in the design of the ambiguity set to reduce conservatism. Particularly, the set specifically constrains the worst-case distribution along the direction in which the expected cost of an approximate solution increases most rapidly. We prove that CADRO provides both a high-confidence upper bound and a consistent estimator of the out-of-sample expected cost, and show empirically that it produces solutions that are substantially less conservative than existing DRO methods, while providing the same guarantees.

翻译：我们提出了一种新的分布鲁棒优化（DRO）框架，称为成本感知分布鲁棒优化（CADRO）。CADRO的核心思想是在模糊集设计中利用成本结构来降低保守性。具体而言，该模糊集专门约束了最坏情况分布的方向，该方向沿着近似解的期望成本增长最快的路径。我们证明CADRO既为样本外期望成本提供了高置信度上界，又提供了一致估计量，并通过实验表明，与现有DRO方法相比，CADRO在提供相同保证的同时，能生成保守性显著更低的解。