  We consider decentralized optimization over time-varying directed networks.
Network nodes can access only their local objectives, and aim to
collaboratively minimize a global function by exchanging messages with their
neighbors. Leveraging sparsification, gradient tracking and variance-reduction,
we propose a novel communication-efficient decentralized optimization scheme
that is suitable for resource-constrained time-varying directed networks. We
prove that in the case of smooth and strongly-convex objective functions, the
proposed scheme achieves an accelerated linear convergence rate. To our
knowledge, this is the first decentralized optimization framework that achieves
such a convergence rate and applies to settings requiring sparsified
communication. Experimental results on both synthetic and real datasets verify
the theoretical results and demonstrate efficacy of the proposed scheme.
