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Adam is the important optimization algorithm to guarantee efficiency andaccuracy for training many important tasks such as BERT and ImageNet. However,Adam is generally not compatible with information (gradient) compressiontechnology. Therefore, the communication usually becomes the bottleneck forparallelizing Adam. In this paper, we propose a communication efficient {\bfA}DAM {\bf p}reconditioned {\bf M}omentum SGD algorithm-- named APMSqueeze--through an error compensated method compressing gradients. The proposedalgorithm achieves a similar convergence efficiency to Adam in term of epochs,but significantly reduces the running time per epoch. In terms of end-to-endperformance (including the full-precision pre-condition step), APMSqueeze isable to provide {sometimes by up to $2-10\times$ speed-up depending on networkbandwidth.} We also conduct theoretical analysis on the convergence andefficiency.

APMSqueeze: A Communication Efficient Adam-Preconditioned Momentum SGD Algorithm