  Modern large scale machine learning applications require stochastic
optimization algorithms to be implemented on distributed computational
architectures. A key bottleneck is the communication overhead for exchanging
information such as stochastic gradients among different workers. In this
paper, to reduce the communication cost we propose a convex optimization
formulation to minimize the coding length of stochastic gradients. To solve the
optimal sparsification efficiently, several simple and fast algorithms are
proposed for approximate solution, with theoretical guaranteed for sparseness.
Experiments on $\ell_2$ regularized logistic regression, support vector
machines, and convolutional neural networks validate our sparsification
approaches.
