Efficient Data-Driven Optimization with Noisy Data

Classical Kullback-Leibler or entropic distances have recently been shown to enjoy certain desirable statistical properties in the context of decision-making with noiseless data. However, a major criticism of such distances is that they may result in fragile decisions in the presence of a distributional shift between the training and out-of-sample data. Instead, we study here data-driven prediction problems with data which is corrupted by noise. 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