We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e., zero-variance) change of measure and exploits the fact that the latter can be rephrased as a stochastic optimal control problem. The control problem can be solved by a stochastic approximation algorithm, using the Feynman–Kac representation of the associated dynamic programming equations, and we discuss numerical aspects for high-dimensional problems along with simple toy examples.
Variational approach to rare event simulation using least-squares regression
Note: This article is part of the Focus Issue on “Rare Event Sampling Methods: Development, Analysis and Application.”
Carsten Hartmann, Omar Kebiri, Lara Neureither, Lorenz Richter; Variational approach to rare event simulation using least-squares regression. Chaos 1 June 2019; 29 (6): 063107. https://doi.org/10.1063/1.5090271
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