Distributionally Robust Decision Making Leveraging Conditional Distributions

Conference · Tue Dec 06 04:00:00 EST 2022 · 2022 IEEE 61st Conference on Decision and Control (CDC)

DOI:https://doi.org/10.1109/cdc51059.2022.9992782· OSTI ID:1989810

Chen, Yuxiao ^[1]; Kim, Jip ^[2]; Anderson, James ^[2]

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1. Nvidia Corporation,Santa Clara,CA,95051; Columbia University
2. Columbia University,New York,NY,10027

Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distributions is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.

• Research Organization: Columbia University
• Sponsoring Organization: USDOE Office of Energy Efficiency and Renewable Energy (EERE)
• DOE Contract Number: EE0008769
• OSTI ID: 1989810
• Conference Information: Journal Name: 2022 IEEE 61st Conference on Decision and Control (CDC)
• Country of Publication: United States
• Language: English