  Large scale machine learning is increasingly relying on distributed
optimization, whereby several machines contribute to the training process of a
statistical model. In this work we study the performance of asynchronous,
distributed settings, when applying sparsification, a technique used to reduce
communication overheads. In particular, for the first time in an asynchronous,
non-convex setting, we theoretically prove that, in presence of staleness,
sparsification does not harm SGD performance: the ergodic convergence rate
matches the known result of standard SGD, that is $\mathcal{O} \left(
1/\sqrt{T} \right)$. We also carry out an empirical study to complement our
theory, and confirm that the effects of sparsification on the convergence rate
are negligible, when compared to 'vanilla' SGD, even in the challenging
scenario of an asynchronous, distributed system.
