Distributionally Robust Optimization via Haar Wavelet Ambiguity Sets

D. Boskos, Jorge Cortes, S. Martinez Sandez

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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Abstract

This paper introduces a spectral parameterization of ambiguity sets to hedge against distributional uncertainty in stochastic optimization problems. We build an ambiguity set of probability densities around a histogram estimator, which is constructed by independent samples from the unknown distribution. The densities in the ambiguity set are determined by bounding the distance between the coefficients of their Haar wavelet expansion and the expansion of the histogram estimator. This representation facilitates the computation of expectations, leading to tractable minimax problems that are linear in the parameters of the ambiguity set, and enables the inclusion of additional constraints that can capture valuable prior information about the unknown distribution.
Original languageEnglish
Title of host publicationProceedings of the IEEE 61st Conference on Decision and Control (CDC 2022)
PublisherIEEE
Pages4782-4787
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

  • Histograms
  • Costs
  • Uncertainty
  • Probabilistic logic
  • Optimization
  • Wavelet coefficients

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