Efficient Data-Driven Optimization with Noisy Data
This work provides a method for decision-makers to handle noisy data in data-driven prescription problems, improving the robustness of optimization outcomes.
This paper addresses data-driven optimization problems where input data is corrupted by known measurement noise. The authors derive efficient, robust formulations that have an entropic optimal transport interpretation and are tractable in several settings.
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.