Decentralized Asynchronous Nonconvex Stochastic Optimization on Directed Graphs

Kungurtsev, Vyacheslav; Morafah, Mahdi; Javidi, Tara; Scutari, Gesualdo

doi:10.1109/tcns.2023.3242043

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…Furthermore, a distributed derivative-free GT algorithm was proposed in [27], where the zero-order stochastic GT estimator is used in the iterations. In [28], the distributed stochastic GT algorithm was also extended to non-convex optimization problems over unbalanced networks. More recently, several variance reduction techniques were employed in distributed GT algorithm to reduce the variances of the stochastic gradient estimators [4], [19], [29].…”

Section: Introductionmentioning

confidence: 99%

Distributed Stochastic Gradient Tracking Algorithm With Variance Reduction for Non-Convex Optimization

Xia

Zeng

Sun

et al. 2023

IEEE Trans. Neural Netw. Learning Syst.

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This paper considers a distributed stochastic nonconvex 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.

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