During this presentation we study multi-level stochastic approximation algorithm. Our aim is to extend the scope of the multi-level Monte Carlo method recently introduced by Giles (Giles 2008) to the framework of stochastic optimization by means of stochastic approximation algorithm. We first introduce and study a two-level method, also referred as statistical romberg stochastic approximation algorithm. Then, its extension to multi-level is proposed. We prove a central limit theorem for both methods and describe the possible optimal choices of step size sequence. Numerical results confirm the theoretical analysis and show a significant reduction in the initial computational cost. If time permits I will present how the principle of Richardson-Romberg extrapolation method can be applied to stochastic optimization.
The seminar will be followed by wine and finger food with the speaker. All attendees are welcome!