  Recently, reducing communication time between machines becomes the main focus
of distributed data mining. Previous methods propose to make workers do more
computation locally before aggregating local solutions in the server such that
fewer communication rounds between server and workers are required. However,
these methods do not consider reducing the communication time per round and
work very poor under certain conditions, for example, when there are straggler
problems or the dataset is of high dimension. In this paper, we target to
reduce communication time per round as well as the required communication
rounds. We propose a communication-efficient distributed primal-dual method
with straggler-agnostic server and bandwidth-efficient workers. We analyze the
convergence property and prove that the proposed method guarantees linear
convergence rate to the optimal solution for convex problems. Finally, we
conduct large-scale experiments in simulated and real distributed systems and
experimental results demonstrate that the proposed method is much faster than
compared methods.
