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In this work we propose a distributed randomized block coordinate descentmethod for minimizing a convex function with a huge number ofvariables/coordinates. We analyze its complexity under the assumption that thesmooth part of the objective function is partially block separable, and showthat the degree of separability directly influences the complexity. Thisextends the results in [Richtarik, Takac: Parallel coordinate descent methodsfor big data optimization] to a distributed environment. We first show thatpartially block separable functions admit an expected separableoverapproximation (ESO) with respect to a distributed sampling, compute the ESOparameters, and then specialize complexity results from recent literature thathold under the generic ESO assumption. We describe several approaches todistribution and synchronization of the computation across a cluster ofmulti-core computers and provide promising computational results.

Distributed Block Coordinate Descent for Minimizing Partially Separable Functions