  Distributed sparse learning with a cluster of multiple machines has attracted
much attention in machine learning, especially for large-scale applications
with high-dimensional data. One popular way to implement sparse learning is to
use $L_1$ regularization. In this paper, we propose a novel method, called
proximal \mbox{SCOPE}~(\mbox{pSCOPE}), for distributed sparse learning with
$L_1$ regularization. pSCOPE is based on a \underline{c}ooperative
\underline{a}utonomous \underline{l}ocal \underline{l}earning~(\mbox{CALL})
framework. In the \mbox{CALL} framework of \mbox{pSCOPE}, we find that the data
partition affects the convergence of the learning procedure, and subsequently
we define a metric to measure the goodness of a data partition. Based on the
defined metric, we theoretically prove that pSCOPE is convergent with a linear
convergence rate if the data partition is good enough. We also prove that
better data partition implies faster convergence rate. Furthermore, pSCOPE is
also communication efficient. Experimental results on real data sets show that
pSCOPE can outperform other state-of-the-art distributed methods for sparse
learning.
