  Stochastic gradient descent (SGD) has taken the stage as the primary
workhorse for large-scale machine learning. It is often used with its adaptive
variants such as AdaGrad, Adam, and AMSGrad. This paper proposes an adaptive
stochastic gradient descent method for distributed machine learning, which can
be viewed as the communication-adaptive counterpart of the celebrated Adam
method - justifying its name CADA. The key components of CADA are a set of new
rules tailored for adaptive stochastic gradients that can be implemented to
save communication upload. The new algorithms adaptively reuse the stale Adam
gradients, thus saving communication, and still have convergence rates
comparable to original Adam. In numerical experiments, CADA achieves impressive
empirical performance in terms of total communication round reduction.
