Distributed Adaptive Gradient Algorithm with Gradient Tracking for Stochastic Non-Convex Optimization

Fuente: arXiv
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Autori principali: Han, Dongyu, Liu, Kun, Lin, Yeming, Xia, Yuanqing
Natura: Preprint
Pubblicazione: 2024
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author Han, Dongyu
Liu, Kun
Lin, Yeming
Xia, Yuanqing
author_facet Han, Dongyu
Liu, Kun
Lin, Yeming
Xia, Yuanqing
contents This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes according to the historical (possibly sparse) gradients, a distributed adaptive gradient algorithm is proposed, in which a gradient tracking estimator is used to handle the heterogeneity between different local cost functions. We establish an upper bound on the optimality gap, which indicates that our proposed algorithm can reach a first-order stationary solution dependent on the upper bound on the variance of the stochastic gradients. Finally, numerical examples are presented to illustrate the effectiveness of the algorithm.
format Preprint
id arxiv_https___arxiv_org_abs_2403_11557
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Distributed Adaptive Gradient Algorithm with Gradient Tracking for Stochastic Non-Convex Optimization
Han, Dongyu
Liu, Kun
Lin, Yeming
Xia, Yuanqing
Optimization and Control
This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes according to the historical (possibly sparse) gradients, a distributed adaptive gradient algorithm is proposed, in which a gradient tracking estimator is used to handle the heterogeneity between different local cost functions. We establish an upper bound on the optimality gap, which indicates that our proposed algorithm can reach a first-order stationary solution dependent on the upper bound on the variance of the stochastic gradients. Finally, numerical examples are presented to illustrate the effectiveness of the algorithm.
title Distributed Adaptive Gradient Algorithm with Gradient Tracking for Stochastic Non-Convex Optimization
topic Optimization and Control
url https://arxiv.org/abs/2403.11557