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In this paper, we establish new convergence results for the quantizeddistributed gradient descent and suggest a novel strategy of choosing thestepsizes for the high-performance of the algorithm. Under the stronglyconvexity assumption on the aggregate cost function and the smoothnessassumption on each local cost function, we prove the algorithm convergesexponentially fast to a small neighborhood of the optimizer whose radiusdepends on the stepsizes. Based on our convergence result, we suggest aneffective selection of stepsizes which repeats diminishing the stepsizes aftera number of specific iterations. Both the convergence results and theeffectiveness of the suggested stepsize selection are also verified by thenumerical experiments.

Convergence property of the Quantized Distributed Gradient descent with constant stepsizes and an effective strategy for the stepsize selection