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：经典库尔贝克-莱布勒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，决策者获取的数据会受到一定程度的测量噪声干扰。因此，本文研究噪声数据受已知噪声源污染时的数据驱动决策问题。我们推导了噪声环境下的高效数据驱动公式，并证明其具有熵最优输运解释。最后，通过利用斯特拉森经典表示定理，我们证明了这些高效稳健公式在若干重要场景下是可解的。