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Stochastic Gradient Descent (SGD) is the key learning algorithm for many machine learning tasks. Because of its computational costs, there is a growing interest in accelerating SGD on HPC resources like GPU clusters. However, the performance of parallel SGD is still bottlenecked by the high communication costs even with a fast connection among the machines. A simple approach to alleviating this problem, used in many existing efforts, is to perform communication every few iterations, using a constant averaging period. In this paper, we show that the optimal averaging period in terms of convergence and communication cost is not a constant, but instead varies over the course of the execution. Specifically, we observe that reducing the variance of model parameters among the computing nodes is critical to the convergence of periodic parameter averaging SGD. Given a fixed communication budget, we show that it is more beneficial to synchronize more frequently in early iterations to reduce the initial large variance and synchronize less frequently in the later phase of the training process. We propose a practical algorithm, named ADaptive Periodic parameter averaging SGD (ADPSGD), to achieve a smaller overall variance of model parameters, and thus better convergence compared with the Constant Periodic parameter averaging SGD (CPSGD). We evaluate our method with several image classification benchmarks and show that our ADPSGD indeed achieves smaller training losses and higher test accuracies with smaller communication compared with CPSGD. Compared with gradient-quantization SGD, we show that our algorithm achieves faster convergence with only half of the communication. Compared with full-communication SGD, our ADPSGD achieves 1:14x to 1:27x speedups with a 100Gbps connection among computing nodes, and the speedups increase to 1:46x ~ 1:95x with a 10Gbps connection.