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Scalable machine learning over big data is an important problem that isreceiving a lot of attention in recent years. On popular distributedenvironments such as Hadoop running on a cluster of commodity machines,communication costs are substantial and algorithms need to be designed suitablyconsidering those costs. In this paper we give a novel approach to thedistributed training of linear classifiers (involving smooth losses and L2regularization) that is designed to reduce the total communication costs. Ateach iteration, the nodes minimize locally formed approximate objectivefunctions; then the resulting minimizers are combined to form a descentdirection to move. Our approach gives a lot of freedom in the formation of theapproximate objective function as well as in the choice of methods to solvethem. The method is shown to have $O(log(1/\epsilon))$ time convergence. Themethod can be viewed as an iterative parameter mixing method. A specialinstantiation yields a parallel stochastic gradient descent method with strongconvergence. When communication times between nodes are large, our method ismuch faster than the Terascale method (Agarwal et al., 2011), which is a stateof the art distributed solver based on the statistical query model (Chuet al.,2006) that computes function and gradient values in a distributed fashion. Wealso evaluate against other recent distributed methods and demonstrate superiorperformance of our method.

An efficient distributed learning algorithm based on effective local functional approximations