Uncertain uncertainty in data-driven stochastic optimization: towards structured ambiguity sets

Conference Paper (2022)
Author(s)

L. Chaouach (TU Delft - Team Dimitris Boskos)

D. Boskos (TU Delft - Team Dimitris Boskos)

Tom Oomen (Eindhoven University of Technology, TU Delft - Team Jan-Willem van Wingerden)

Research Group
Team Dimitris Boskos
Copyright
© 2022 L. Chaouach, D. Boskos, T.A.E. Oomen
DOI related publication
https://doi.org/10.1109/CDC51059.2022.9992405
More Info
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Publication Year
2022
Language
English
Copyright
© 2022 L. Chaouach, D. Boskos, T.A.E. Oomen
Research Group
Team Dimitris Boskos
Pages (from-to)
4776-4781
ISBN (print)
978-1-6654-6761-2
Reuse Rights

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Abstract

Ambiguity sets of probability distributions are a prominent tool to hedge against distributional uncertainty in stochastic optimization. The aim of this paper is to build tight Wasserstein ambiguity sets for data-driven optimization problems. The method exploits independence between the distribution components to introduce structure in the ambiguity sets and speed up their shrinkage with the number of collected samples. Tractable reformulations of the stochastic optimization problems are derived for costs that are expressed as sums or products of functions that depend only on the individual distribution components. The statistical benefits of the approach are theoretically analyzed for compactly supported distributions and demonstrated in a numerical example.

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