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

L. Chaouach; D. Boskos; T.A.E. Oomen

doi:10.1109/CDC51059.2022.9992405

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

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

2 Citations (Scopus)

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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 language	English
Title of host publication	Proceedings of the IEEE 61st Conference on Decision and Control (CDC 2022)
Publisher	IEEE
Pages	4776-4781
ISBN (Print)	978-1-6654-6761-2
DOIs	https://doi.org/10.1109/CDC51059.2022.9992405
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

Uncertainty
Costs
Cost function
Probability distribution
Random variables

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10.1109/CDC51059.2022.9992405

Uncertain_uncertainty_in_data-driven_stochastic_optimization_towards_structured_ambiguity_setsFinal published version, 1.35 MB

Cite this

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title = "Uncertain uncertainty in data-driven stochastic optimization: towards structured ambiguity sets",

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.",

keywords = "Uncertainty, Costs, Cost function, Probability distribution, Random variables",

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doi = "10.1109/CDC51059.2022.9992405",

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AU - Boskos, D.

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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

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N2 - 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.

AB - 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.

KW - Uncertainty

KW - Costs

KW - Cost function

KW - Probability distribution

KW - Random variables

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DO - 10.1109/CDC51059.2022.9992405

M3 - Conference contribution

SN - 978-1-6654-6761-2

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EP - 4781

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

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

Y2 - 6 December 2022 through 9 December 2022

ER -

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

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Bibliographical note

Keywords

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