Classical Kullback-Leibler or entropic distances are known to enjoy certain desirable statistical properties in the context of decision-making with noiseless data. However, in most practical situations the data available to a decision maker is subject to a certain amount of measurement noise. We hence study here data-driven prescription problems in which the data is corrupted by a known noise source. We derive efficient data-driven formulations in this noisy regime and indicate that they enjoy an entropic optimal transport interpretation. Finally, we show that these efficient robust formulations are tractable in several interesting settings by exploiting a classical representation result by Strassen.

翻译：经典Kullback-Leibler距离或熵距离在无噪声数据决策背景下具有某些理想的统计特性。然而，在大多数实际场景中，决策者可获取的数据都会受到一定程度的测量噪声污染。因此，本文研究数据被已知噪声源污染的数据驱动制定问题。我们在含噪情形下推导出高效的数据驱动公式，并指出它们具有熵最优传输解释。最后，我们通过利用Strassen的经典表示结果，证明这些高效鲁棒公式在多个有趣场景中是可解的。