  We consider a decentralized learning problem, where a set of computing nodes
aim at solving a non-convex optimization problem collaboratively. It is
well-known that decentralized optimization schemes face two major system
bottlenecks: stragglers' delay and communication overhead. In this paper, we
tackle these bottlenecks by proposing a novel decentralized and gradient-based
optimization algorithm named as QuanTimed-DSGD. Our algorithm stands on two
main ideas: (i) we impose a deadline on the local gradient computations of each
node at each iteration of the algorithm, and (ii) the nodes exchange quantized
versions of their local models. The first idea robustifies to straggling nodes
and the second alleviates communication efficiency. The key technical
contribution of our work is to prove that with non-vanishing noises for
quantization and stochastic gradients, the proposed method exactly converges to
the global optimal for convex loss functions, and finds a first-order
stationary point in non-convex scenarios. Our numerical evaluations of the
QuanTimed-DSGD on training benchmark datasets, MNIST and CIFAR-10, demonstrate
speedups of up to 3x in run-time, compared to state-of-the-art decentralized
optimization methods.
