Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation

Understand

In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC).

• We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the different levels independently.
• The search for parameters is carried out using sample average approximation, which basically consists in applying deterministic optimisation techniques to a Monte Carlo approximation rather than resorting to stochastic approximation.
• Our innovative estimator leads to a robust and efficient procedure reducing both the discretization error (the bias) and the variance for a given computational effort.