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General multilevel adaptations for stochastic approximation algorithms II: CLTs

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  • Dereich, Steffen

Abstract

In this article we establish central limit theorems for multilevel Polyak–Ruppert averaged stochastic approximation schemes. We work under very mild technical assumptions and consider the slow regime in which typical errors decay like N−δ with δ∈(0,12) and the critical regime in which errors decay of order N−1∕2logN in the runtime N of the algorithm.

Suggested Citation

  • Dereich, Steffen, 2021. "General multilevel adaptations for stochastic approximation algorithms II: CLTs," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 226-260.
    • Handle: RePEc:eee:spapps:v:132:y:2021:i:c:p:226-260
    DOI: 10.1016/j.spa.2020.11.001
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    References listed on IDEAS

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    1. McLeish, Don, 2011. "A general method for debiasing a Monte Carlo estimator," Monte Carlo Methods and Applications, De Gruyter, vol. 17(4), pages 301-315, December.
    2. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    3. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
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    Cited by:

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    2. Jingxu Xu & Zeyu Zheng, 2023. "Gradient-Based Simulation Optimization Algorithms via Multi-Resolution System Approximations," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 633-651, May.

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