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Distributed stochastic gradient tracking methods with momentum acceleration for non-convex optimization

Juan Gao (), Xin-Wei Liu (), Yu-Hong Dai (), Yakui Huang () and Junhua Gu ()
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Juan Gao: Hebei University of Technology
Xin-Wei Liu: Hebei University of Technology
Yu-Hong Dai: Chinese Academy of Sciences
Yakui Huang: Hebei University of Technology
Junhua Gu: Hebei University of Technology

Computational Optimization and Applications, 2023, vol. 84, issue 2, No 9, 572 pages

Abstract: Abstract We consider a distributed non-convex optimization problem of minimizing the sum of all local cost functions over a network of agents. This problem often appears in large-scale distributed machine learning, known as non-convex empirical risk minimization. In this paper, we propose two accelerated algorithms, named DSGT-HB and DSGT-NAG, which combine the distributed stochastic gradient tracking (DSGT) method with momentum accelerated techniques. Under appropriate assumptions, we prove that both algorithms sublinearly converge to a neighborhood of a first-order stationary point of the distributed non-convex optimization. Moreover, we derive the conditions under which DSGT-HB and DSGT-NAG achieve a network-independent linear speedup. Numerical experiments for a distributed non-convex logistic regression problem on real data sets and a deep neural network on the MNIST database show the superiorities of DSGT-HB and DSGT-NAG compared with DSGT.

Keywords: Distributed non-convex optimization; Machine learning; Momentum methods; Optimization algorithms; Convergence rate (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-022-00432-5

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