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Several works have shown linear speedup is achieved by an asynchronousparallel implementation of stochastic coordinate descent so long as there isnot too much parallelism. More specifically, it is known that if all updatesare of similar duration, then linear speedup is possible with up to$\Theta(\sqrt n L_{\max}/L_{\overline{\mathrm{res}}})$ processors, where$L_{\max}$ and $L_{\overline{\mathrm{res}}}$ are suitable Lipschitz parameters.This paper shows the bound is tight for almost all possible values of theseparameters.

Parallel Stochastic Asynchronous Coordinate Descent: Tight Bounds on the Possible Parallelism