  Bootstrap is a principled and powerful frequentist statistical tool for
uncertainty quantification. Unfortunately, standard bootstrap methods are
computationally intensive due to the need of drawing a large i.i.d. bootstrap
sample to approximate the ideal bootstrap distribution; this largely hinders
their application in large-scale machine learning, especially deep learning
problems. In this work, we propose an efficient method to explicitly
\emph{optimize} a small set of high quality ``centroid'' points to better
approximate the ideal bootstrap distribution. We achieve this by minimizing a
simple objective function that is asymptotically equivalent to the Wasserstein
distance to the ideal bootstrap distribution. This allows us to provide an
accurate estimation of uncertainty with a small number of bootstrap centroids,
outperforming the naive i.i.d. sampling approach. Empirically, we show that our
method can boost the performance of bootstrap in a variety of applications.
