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

Autor:	Choi, Woocheol, Lee, Myeong-Su
Rok vydání:	2023
Předmět:	Mathematics - Optimization and Control 65K10 90C25 68W15 68W40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.17481 Zobrazit plný text záznamu View this record from Arxiv