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Improving the stochastically controlled stochastic gradient method by the bandwidth-based stepsize

Author

Listed:
  • Chenchen Liu

    (Hebei University of Technology)

  • Yakui Huang

    (Hebei University of Technology
    Hebei University of Technology)

  • Dan Wang

    (Hebei University of Technology)

Abstract

Stepsize plays an important role in the stochastic gradient method. The bandwidth-based stepsize allows us to adjust the stepsize within a banded region determined by some boundary functions. Based on the bandwidth-based stepsize, we propose a new method, namely SCSG-BD, for smooth non-convex finite-sum optimization problems. For the boundary functions 1/t, $$1/(t\log (t + 1))$$ 1 / ( t log ( t + 1 ) ) and $$1/t^p$$ 1 / t p ( $$p\in (0,1)$$ p ∈ ( 0 , 1 ) ), SCSG-BD converges sublinearly to a stationary point at a faster rate than the stochastically controlled stochastic gradient (SCSG) method under certain conditions. Moreover, SCSG-BD is able to converge linearly to the solution if the objective function satisfies the Polyak–Łojasiewicz condition. We also introduce the 1/t-Barzilai–Borwein stepsize for practical computation. Numerical experiments demonstrate that SCSG-BD performs better than SCSG and its variants.

Suggested Citation

  • Chenchen Liu & Yakui Huang & Dan Wang, 2025. "Improving the stochastically controlled stochastic gradient method by the bandwidth-based stepsize," Computational Optimization and Applications, Springer, vol. 90(3), pages 941-968, April.
    • Handle: RePEc:spr:coopap:v:90:y:2025:i:3:d:10.1007_s10589-025-00651-6
    DOI: 10.1007/s10589-025-00651-6
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