Consistent Adaptive Multiple Importance Sampling and Controlled Diffusions

Abstract: Recent progress has been made with Adaptive Multiple Importance Sampling (AMIS) methods that show improvement in effective sample size. However, consistency for the AMIS estimator has only been established in very restricted cases. Furthermore, the high computational complexity of the re-weighting in AMIS (called balance heuristic) makes it expensive for applications involving diffusion processes. In this work we consider sequential and adaptive importance sampling that is particularly suitable for diffusion processes. We propose a new discarding-re-weighting scheme that is of lower computational complexity, and we prove that the resulting AMIS is consistent. Using numerical experiments, we demonstrate that discarding-re-weighting performs very similar to the balance heuristic, but at a fraction of the computational cost.