  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.
