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

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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.
Original languageEnglish
Title of host publicationProceedings of the IEEE 61st Conference on Decision and Control (CDC 2022)
PublisherIEEE
Pages4776-4781
ISBN (Print)978-1-6654-6761-2
DOIs
Publication statusPublished - 2022
EventIEEE 61st Conference on Decision and Control (CDC 2022) - Cancún, Mexico
Duration: 6 Dec 20229 Dec 2022

Conference

ConferenceIEEE 61st Conference on Decision and Control (CDC 2022)
Country/TerritoryMexico
CityCancún
Period6/12/229/12/22

Bibliographical note

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.

Keywords

  • Uncertainty
  • Costs
  • Cost function
  • Probability distribution
  • Random variables

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