  Decentralized training has been actively studied in recent years. Although a
wide variety of methods have been proposed, yet the decentralized momentum SGD
method is still underexplored. In this paper, we propose a novel periodic
decentralized momentum SGD method, which employs the momentum schema and
periodic communication for decentralized training. With these two strategies,
as well as the topology of the decentralized training system, the theoretical
convergence analysis of our proposed method is difficult. We address this
challenging problem and provide the condition under which our proposed method
can achieve the linear speedup regarding the number of workers. Furthermore, we
also introduce a communication-efficient variant to reduce the communication
cost in each communication round. The condition for achieving the linear
speedup is also provided for this variant. To the best of our knowledge, these
two methods are all the first ones achieving these theoretical results in their
corresponding domain. We conduct extensive experiments to verify the
performance of our proposed two methods, and both of them have shown superior
performance over existing methods.
