Distributionally Robust Optimization via Haar Wavelet Ambiguity Sets

D. Boskos; Jorge Cortes; S. Martinez Sandez

doi:10.1109/CDC51059.2022.9993084

Distributionally Robust Optimization via Haar Wavelet Ambiguity Sets

D. Boskos, Jorge Cortes, S. Martinez Sandez

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

1 Citation (Scopus)

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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 language	English
Title of host publication	Proceedings of the IEEE 61st Conference on Decision and Control (CDC 2022)
Publisher	IEEE
Pages	4782-4787
ISBN (Print)	978-1-6654-6761-2
DOIs	https://doi.org/10.1109/CDC51059.2022.9993084
Publication status	Published - 2022
Event	IEEE 61st Conference on Decision and Control (CDC 2022) - Cancún, Mexico Duration: 6 Dec 2022 → 9 Dec 2022

Conference

Conference	IEEE 61st Conference on Decision and Control (CDC 2022)
Country/Territory	Mexico
City	Cancún
Period	6/12/22 → 9/12/22

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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10.1109/CDC51059.2022.9993084

Distributionally_Robust_Optimization_via_Haar_Wavelet_Ambiguity_SetsFinal published version, 1.08 MB

Cite this

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title = "Distributionally Robust Optimization via Haar Wavelet Ambiguity Sets",

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.",

keywords = "Histograms, Costs, Uncertainty, Probabilistic logic, Optimization, Wavelet coefficients",

author = "D. Boskos and Jorge Cortes and {Martinez Sandez}, S.",

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.; IEEE 61st Conference on Decision and Control (CDC 2022) ; Conference date: 06-12-2022 Through 09-12-2022",

year = "2022",

doi = "10.1109/CDC51059.2022.9993084",

language = "English",

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AU - Cortes, Jorge

AU - Martinez Sandez, S.

N1 - 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.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Histograms

KW - Costs

KW - Uncertainty

KW - Probabilistic logic

KW - Optimization

KW - Wavelet coefficients

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U2 - 10.1109/CDC51059.2022.9993084

DO - 10.1109/CDC51059.2022.9993084

M3 - Conference contribution

SN - 978-1-6654-6761-2

SP - 4782

EP - 4787

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

PB - IEEE

T2 - IEEE 61st Conference on Decision and Control (CDC 2022)

Y2 - 6 December 2022 through 9 December 2022

ER -

Distributionally Robust Optimization via Haar Wavelet Ambiguity Sets

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Bibliographical note

Keywords

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