Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

Li, Qi; Liang, Zhirui; Bernstein, Andrey; Dvorkin, Yury

doi:10.1109/LCSYS.2024.3407629

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

Journal Article · Thu May 30 04:00:00 EDT 2024 · IEEE Control Systems Letters

DOI:https://doi.org/10.1109/LCSYS.2024.3407629· OSTI ID:2376667

Li, Qi; Liang, Zhirui; Bernstein, Andrey; Dvorkin, Yury

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

Research Organization:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Organization:: USDOE National Renewable Energy Laboratory (NREL)

DOE Contract Number:: AC36-08GO28308

OSTI ID:: 2376667

Report Number(s):: NREL/JA-5D00-90211; MainId:91989; UUID:5e6fb08e-f6b6-41ff-a3a1-2d156bd3998f; MainAdminId:72805

Journal Information:: IEEE Control Systems Letters, Journal Name: IEEE Control Systems Letters Vol. 8

Country of Publication:: United States

Language:: English

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Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

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