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Distributed sparse learning with a cluster of multiple machines has attractedmuch attention in machine learning, especially for large-scale applicationswith high-dimensional data. One popular way to implement sparse learning is touse $L_1$ regularization. In this paper, we propose a novel method, calledproximal \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 datapartition affects the convergence of the learning procedure, and subsequentlywe define a metric to measure the goodness of a data partition. Based on thedefined metric, we theoretically prove that pSCOPE is convergent with a linearconvergence rate if the data partition is good enough. We also prove thatbetter data partition implies faster convergence rate. Furthermore, pSCOPE isalso communication efficient. Experimental results on real data sets show thatpSCOPE can outperform other state-of-the-art distributed methods for sparselearning.

Proximal SCOPE for Distributed Sparse Learning: Better Data Partition Implies Faster Convergence Rate