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

Lotfi M. Chaouach; Dimitris Boskos; Tom Oomen

doi:10.1109/CDC51059.2022.9992405

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

Lotfi M. Chaouach, Dimitris Boskos, Tom Oomen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

4 Citations (Scopus)

229 Downloads (Pure)

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	61th IEEE Conference on Decision and Control 2022
Publisher	Institute of Electrical and Electronics Engineers
Pages	4776-4781
Number of pages	6
ISBN (Electronic)	978-1-6654-6761-2
DOIs	https://doi.org/10.1109/CDC51059.2022.9992405
Publication status	Published - 10 Jan 2023
Event	61st IEEE Conference on Decision and Control, CDC 2022 - The Marriott Cancún Collection, Cancun, Mexico Duration: 6 Dec 2022 → 9 Dec 2022 Conference number: 61 https://cdc2022.ieeecss.org/

Conference

Conference	61st IEEE Conference on Decision and Control, CDC 2022
Abbreviated title	CDC 2022
Country/Territory	Mexico
City	Cancun
Period	6/12/22 → 9/12/22
Internet address	https://cdc2022.ieeecss.org/

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10.1109/CDC51059.2022.9992405

ChaouachBosOom2022bFinal author version , 679 KB

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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.",

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Chaouach, LM, Boskos, D & Oomen, T 2023, Uncertain uncertainty in data-driven stochastic optimization: Towards structured ambiguity sets. in 61th IEEE Conference on Decision and Control 2022., 9992405, Institute of Electrical and Electronics Engineers, pp. 4776-4781, 61st IEEE Conference on Decision and Control, CDC 2022, Cancun, Mexico, 6/12/22. https://doi.org/10.1109/CDC51059.2022.9992405

Uncertain uncertainty in data-driven stochastic optimization: Towards structured ambiguity sets. / Chaouach, Lotfi M.; Boskos, Dimitris; Oomen, Tom.
61th IEEE Conference on Decision and Control 2022. Institute of Electrical and Electronics Engineers, 2023. p. 4776-4781 9992405.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Boskos, Dimitris

AU - Oomen, Tom

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PY - 2023/1/10

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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.

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DO - 10.1109/CDC51059.2022.9992405

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PB - Institute of Electrical and Electronics Engineers

Y2 - 6 December 2022 through 9 December 2022

ER -

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

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