Adaptive importance sampling with forward-backward stochastic differential equations

TL;DR

This paper introduces an adaptive importance sampling method for rare event simulation using forward-backward stochastic differential equations, optimizing path sampling through stochastic control and efficient numerical algorithms.

Contribution

It presents a novel approach combining stochastic control and forward-backward SDEs for adaptive importance sampling in rare event estimation.

Findings

Efficient solution of semi-linear dynamic programming equations via forward-backward SDEs.

Implementation of a least squares Monte Carlo algorithm for high-dimensional systems.

Numerical example demonstrating the effectiveness of the proposed method.

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.