We present a novel class of ambiguity sets for distributionally robust optimization (DRO). These ambiguity sets, called cost-aware ambiguity sets, are defined as halfspaces which depend on the cost function evaluated at an independent estimate of the optimal solution, thus excluding only those distributions that are expected to have significant impact on the obtained worst-case cost. We show that the resulting DRO method provides both a high-confidence upper bound and a consistent estimator of the out-of-sample expected cost, and demonstrate empirically that it results in less conservative solutions compared to divergence-based ambiguity sets.

翻译：我们提出了一类新颖的分布鲁棒优化（DRO）模糊集。这类被称为成本感知模糊集的模糊集，被定义为依赖于独立估计的最优解处成本函数评估的半空间，从而仅排除那些预期会对所得最坏情况成本产生显著影响的分布。我们证明，由此产生的DRO方法既能提供高置信度的上界，又能提供样本外期望成本的一致估计，并通过实证表明，与基于散度的模糊集相比，该方法能得出更为不保守的解。