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

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

Chaouach, L. (TU Delft Team Dimitris Boskos)
Boskos, D. (TU Delft Team Dimitris Boskos)
Oomen, T.A.E. (TU Delft Team Jan-Willem van Wingerden; Eindhoven University of Technology)

2022

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.

Uncertainty
Costs
Cost function
Probability distribution
Random variables

http://resolver.tudelft.nl/uuid:527386b7-96c6-4b0a-8284-8135fcb5e52c

https://doi.org/10.1109/CDC51059.2022.9992405

IEEE

2023-07-10

978-1-6654-6761-2

Proceedings of the IEEE 61st Conference on Decision and Control (CDC 2022)

IEEE 61st Conference on Decision and Control (CDC 2022), 2022-12-06 → 2022-12-09, Cancún, Mexico

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

conference paper

© 2022 L. Chaouach, D. Boskos, T.A.E. Oomen