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Stochastic Gradient Hamiltonian Monte Carlo for non-convex learning

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  • Chau, Huy N.
  • Rásonyi, Miklós

Abstract

Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) is a momentum version of stochastic gradient descent with properly injected Gaussian noise to find a global minimum. In this paper, non-asymptotic convergence analysis of SGHMC is given in the context of non-convex optimization, where subsampling techniques are used over an i.i.d. dataset for gradient updates. In contrast to Raginsky et al. (2017) and Gao et al. (2021), our results are sharper in terms of step size, variance, and independent from the number of iterations.

Suggested Citation

  • Chau, Huy N. & Rásonyi, Miklós, 2022. "Stochastic Gradient Hamiltonian Monte Carlo for non-convex learning," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 341-368.
    • Handle: RePEc:eee:spapps:v:149:y:2022:i:c:p:341-368
    DOI: 10.1016/j.spa.2022.04.001
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    References listed on IDEAS

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    1. Dalalyan, Arnak S. & Karagulyan, Avetik, 2019. "User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5278-5311.
    2. Arnak S. Dalalyan, 2017. "Theoretical guarantees for approximate sampling from smooth and log-concave densities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 651-676, June.
    3. Arnak Dalalyan, 2017. "Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent," Working Papers 2017-21, Center for Research in Economics and Statistics.
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