Data-driven Stochastic Programming with Distributionally Robust Constraints Under Wasserstein Distance: Asymptotic Properties

Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown. We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints. The ambiguity s...

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Bibliographic Details
Published in:Journal of the Operations Research Society of China (Internet) 2021-09, Vol.9 (3), p.525-542
Main Authors: Mei, Yu, Chen, Zhi-Ping, Ji, Bing-Bing, Xu, Zhu-Jia, Liu, Jia
Format: Article
Language:English
Subjects:
Approximation
Asymptotic properties
Convergence
Linear programming
Mathematical functions
Optimization
Random variables
Robustness (mathematics)
Stochastic programming
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Summary:Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown. We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints. The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution. Based on the concentration inequality of Wasserstein distance, we establish the asymptotic convergence property of the data-driven distributionally robust optimization problem when the sample size goes to infinity. We show that with probability 1, the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution. Finally, we provide numerical evidences for the established theoretical results.
ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-020-00313-w