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Diffusion-LSVRG-UP: Distributed LSVRG-based diffusion algorithm with uncoordinated probabilities
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DOI：10.1016/j.jfranklin.2026.108658.png)
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Abstract
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This paper concentrates on large-scale distributed stochastic optimization problems under strongly connected networks. Most of the first-order algorithms designed for distributed optimization use a full gradient to perform a descent step, which would cost huge amounts of time and resources. Therefore, the use of stochastic gradients helps enhance efficiency, in which loopless stochastic variance-reduced gradient (LSVRG) is an excellent choice for gradient estimation. Moreover, compared to gradient tracking algorithms, the Diffusion strategy is adapted for faster convergence and less communication. Therefore, Diffusion-LSVRG-UP is devised in this paper, where ”UP” is an uncoordinated probabilistic triggered mechanism that permits Diffusion-LSVRG-UP to be flexible and more independent of global parameters in the distributed setting. With a feasible range of step-size, the proposed algorithm uses a constant step-size to achieve linear convergence in expectation under strong convexity. To further extend the practical applicability of the algorithm, we replace the strong convexity condition with the Polyak-Łojasiewicz(PL) condition and prove that the algorithm can still achieve linear convergence to the neigborhood of the optimal under this nonconvex condition. In the last part of the paper, several numerical experiments are conducted to validate the convergence and the advantages of Diffusion-LSVRG-UP.
Keywords:
Distributed stochastic optimization
LSVRG
Diffusion strategy
Uncoordinated probabilistic triggering
Linear convergence
Journal
J
IF:
4.2
Papers:
822
Citations:
0
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