  We study COMP-AMS, a distributed optimization framework based on gradient
averaging and adaptive AMSGrad algorithm. Gradient compression with error
feedback is applied to reduce the communication cost in the gradient
transmission process. Our convergence analysis of COMP-AMS shows that such
compressed gradient averaging strategy yields same convergence rate as standard
AMSGrad, and also exhibits the linear speedup effect w.r.t. the number of local
workers. Compared with recently proposed protocols on distributed adaptive
methods, COMP-AMS is simple and convenient. Numerical experiments are conducted
to justify the theoretical findings, and demonstrate that the proposed method
can achieve same test accuracy as the full-gradient AMSGrad with substantial
communication savings. With its simplicity and efficiency, COMP-AMS can serve
as a useful distributed training framework for adaptive gradient methods.
