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

TL;DR

This paper proves exponential convergence of quantized distributed gradient descent with constant stepsizes under certain conditions and proposes a practical stepsize selection strategy that enhances algorithm performance.

Contribution

It introduces new convergence results for quantized distributed gradient descent and a novel stepsize selection method to improve efficiency.

Findings

Algorithm converges exponentially to a neighborhood of the optimizer.

The suggested stepsize strategy improves convergence speed.

Numerical experiments confirm theoretical results.

Abstract

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.