A MULTI-STEP RICHARDSON-ROMBERG EXTRAPOLATION METHOD FOR STOCHASTIC APPROXIMATION

Noufel Frikha (1) , Lorick Huang (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in [Frikha2013]. This allows us to extend and develop the Richardson-Romberg extrapolation method for Monte Carlo linear estimator (introduced in [Talay & 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.

Mots clés: Euler scheme; weak error; Richardson-Romberg extrapolation; stochastic approximation algorithm

Domaines: Probabilités [math.PR]

Noufel Frikha, Lorick Huang. A MULTI-STEP RICHARDSON-ROMBERG EXTRAPOLATION METHOD FOR STOCHASTIC APPROXIMATION. 2014. ⟨hal-01064536v1⟩