  A wide range of optimization problems arising in machine learning can be
solved by gradient descent algorithms, and a central question in this area is
how to efficiently compress a large-scale dataset so as to reduce the
computational complexity. {\em Coreset} is a popular data compression technique
that has been extensively studied before. However, most of existing coreset
methods are problem-dependent and cannot be used as a general tool for a
broader range of applications. A key obstacle is that they often rely on the
pseudo-dimension and total sensitivity bound that can be very high or hard to
obtain. In this paper, based on the ''locality'' property of gradient descent
algorithms, we propose a new framework, termed ''sequential coreset'', which
effectively avoids these obstacles. Moreover, our method is particularly
suitable for sparse optimization whence the coreset size can be further reduced
to be only poly-logarithmically dependent on the dimension. In practice, the
experimental results suggest that our method can save a large amount of running
time compared with the baseline algorithms.
