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A multi-step Richardson–Romberg extrapolation method for stochastic approximation

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  • Frikha, N.
  • Huang, L.

Abstract

We obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in Frikha (2013). This allows us to extend and develop the Richardson–Romberg extrapolation method for Monte Carlo linear estimator (introduced in Talay and Tubaro (1990) and deeply studied in Pagès (2007)) to the framework of stochastic optimization by means of stochastic approximation algorithm. We notably apply the method to the estimation of the quantile of diffusion processes. Numerical results confirm the theoretical analysis and show a significant reduction in the initial computational cost.

Suggested Citation

  • Frikha, N. & Huang, L., 2015. "A multi-step Richardson–Romberg extrapolation method for stochastic approximation," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4066-4101.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:11:p:4066-4101
    DOI: 10.1016/j.spa.2015.05.016
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    References listed on IDEAS

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    1. Talay, Denis & Zheng, Ziyu, 2004. "Approximation of quantiles of components of diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 23-46, January.
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    Cited by:

    1. Gadat, Sébastien & Costa, Manon & Huang, Lorick, 2022. "CV@R penalized portfolio optimization with biased stochastic mirror descent," TSE Working Papers 22-1342, Toulouse School of Economics (TSE), revised Nov 2023.

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