  In this paper, we establish new convergence results for the quantized
distributed gradient descent and suggest a novel strategy of choosing the
stepsizes for the high-performance of the algorithm. Under the strongly
convexity assumption on the aggregate cost function and the smoothness
assumption on each local cost function, we prove the algorithm converges
exponentially fast to a small neighborhood of the optimizer whose radius
depends on the stepsizes. Based on our convergence result, we suggest an
effective selection of stepsizes which repeats diminishing the stepsizes after
a number of specific iterations. Both the convergence results and the
effectiveness of the suggested stepsize selection are also verified by the
numerical experiments.

Optimization and Control