We develop and study the iteration complexity of a class of randomized parallel lock-free (asynchronous) first-order methods applied to the problem of minimizing a partially separable convex function. Our methods are especially well suited for big data optimization applications.
In special cases our generic algorithm reduces to parallel gradient descent, parallel stochastic gradient descent, parallel randomized block coordinate descent and Hogwild! . In all cases our results are the first complexity estimates for lock-free variants of the methods, with the exception of Hogwild!, which was analyzed before, and for which we give vastly improved complexity results.
We contrast the approach with the efficiency of synchronous parallel coordinate descent methods  applied to the same problem.
 F. Niu, B. Recht, C. Re, and S. Wright, Hogwild!: A lock-free approach to parallelizing stochastic gradient descent, NIPS 2011.
 P. Richtarik and M. Takac, Parallel coordinate descent methods for big data optimization, arXiv:1212:0873, 2012.
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