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Coresets for Wasserstein Distributionally Robust Optimization Problems
Ruomin Huang · Jiawei Huang · Wenjie Liu · Hu Ding

Wed Dec 07 05:00 PM -- 07:00 PM (PST) @
Wasserstein distributionally robust optimization (\textsf{WDRO}) is a popular model to enhance the robustness of machine learning with ambiguous data. However, the complexity of \textsf{WDRO} can be prohibitive in practice since solving its ``minimax'' formulation requires a great amount of computation. Recently, several fast \textsf{WDRO} training algorithms for some specific machine learning tasks (e.g., logistic regression) have been developed. However, the research on designing efficient algorithms for general large-scale \textsf{WDRO}s is still quite limited, to the best of our knowledge. \textit{Coreset} is an important tool for compressing large dataset, and thus it has been widely applied to reduce the computational complexities for many optimization problems. In this paper, we introduce a unified framework to construct the $\epsilon$-coreset for the general \textsf{WDRO} problems. Though it is challenging to obtain a conventional coreset for \textsf{WDRO} due to the uncertainty issue of ambiguous data, we show that we can compute a ``dual coreset'' by using the strong duality property of \textsf{WDRO}. Also, the error introduced by the dual coreset can be theoretically guaranteed for the original \textsf{WDRO} objective. To construct the dual coreset, we propose a novel grid sampling approach that is particularly suitable for the dual formulation of \textsf{WDRO}. Finally, we implement our coreset approach and illustrate its effectiveness for several \textsf{WDRO} problems in the experiments. See \href{https://arxiv.org/abs/2210.04260}{arXiv:2210.04260} for the full version of this paper. The code is available at \url{https://github.com/h305142/WDRO_coreset}.

Author Information

Ruomin Huang (University of Science and Technology of China)
Jiawei Huang (university of science and technology of china)
Wenjie Liu (University of Science and Technology of China)
Hu Ding (University of Science and Technology of China)

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