Distributed Adaptive Gradient Algorithm with Gradient Tracking for Stochastic Non-Convex Optimization
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911818694262784 |
|---|---|
| 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 |