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!
University Paris VII
Thu, 30/07/2015 - 4:00pm
RC-M032, Red Centre, UNSW