Variational approach to rare event simulation using least-squares regression

26 Jan 2019  ·  Carsten Hartmann, Omar Kebiri, Lara Neureither, Lorenz Richter ·

We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a 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.

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Probability Optimization and Control 65C05 (primary), 65C30, 92C40 (secondary)