Adaptive importance sampling with forward-backward stochastic differential equations
Abstract
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating functions, which appear relevant in the context of, e.g.~molecular dynamics, and we discuss the construction of an optimal (i.e. minimum variance) change of measure by solving a stochastic control problem. We show that the associated semi-linear dynamic programming equations admit an equivalent formulation as a system of uncoupled forward-backward stochastic differential equations that can be solved efficiently by a least squares Monte Carlo algorithm. We illustrate the approach with a suitable numerical example and discuss the extension of the algorithm to high-dimensional systems.
Cite
@article{arxiv.1802.04981,
title = {Adaptive importance sampling with forward-backward stochastic differential equations},
author = {Omar Kebiri and Lara Neureither and Carsten Hartmann},
journal= {arXiv preprint arXiv:1802.04981},
year = {2019}
}