  Stochastic gradient descent (SGD) is one of the most widely used optimization
methods for parallel and distributed processing of large datasets. One of the
key limitations of distributed SGD is the need to regularly communicate the
gradients between different computation nodes. To reduce this communication
bottleneck, recent work has considered a one-bit variant of SGD, where only the
sign of each gradient element is used in optimization. In this paper, we extend
this idea by proposing a stochastic variant of the proximal-gradient method
that also uses one-bit per update element. We prove the theoretical convergence
of the method for non-convex optimization under a set of explicit assumptions.
Our results indicate that the compressed method can match the convergence rate
of the uncompressed one, making the proposed method potentially appealing for
distributed processing of large datasets.
