Efficient Data-Driven Optimization with Noisy Data
Optimization and Control
2024-02-26 v4 Machine Learning
Statistics Theory
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2102.04363,
title = {Efficient Data-Driven Optimization with Noisy Data},
author = {Bart P. G. Van Parys},
journal= {arXiv preprint arXiv:2102.04363},
year = {2024}
}