Wasserstein distributionally robust optimization and its tractable regularization formulations
arxiv(2024)
摘要
We study a variety of Wasserstein distributionally robust optimization (WDRO)
problems where the distributions in the ambiguity set are chosen by
constraining their Wasserstein discrepancies to the empirical distribution.
Using the notion of weak Lipschitz property, we derive lower and upper bounds
of the corresponding worst-case loss quantity and propose sufficient conditions
under which this quantity coincides with its regularization scheme counterpart.
Our constructive methodology and elementary analysis also directly characterize
the closed-form of the approximate worst-case distribution. Extensive
applications show that our theoretical results are applicable to various
problems, including regression, classification and risk measure problems.
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