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Distributed training of $l_1$ regularized classifiers has received greatattention recently. Most existing methods approach this problem by taking stepsobtained from approximating the objective by a quadratic approximation that isdecoupled at the individual variable level. These methods are designed formulticore and MPI platforms where communication costs are low. They areinefficient on systems such as Hadoop running on a cluster of commoditymachines where communication costs are substantial. In this paper we design adistributed algorithm for $l_1$ regularization that is much better suited forsuch systems than existing algorithms. A careful cost analysis is used tosupport these points and motivate our method. The main idea of our algorithm isto do block optimization of many variables on the actual objective functionwithin each computing node; this increases the computational cost per step thatis matched with the communication cost, and decreases the number of outeriterations, thus yielding a faster overall method. Distributed Gauss-Seidel andGauss-Southwell greedy schemes are used for choosing variables to update ineach step. We establish global convergence theory for our algorithm, includingQ-linear rate of convergence. Experiments on two benchmark problems show ourmethod to be much faster than existing methods.

A distributed block coordinate descent method for training $l_1$ regularized linear classifiers