Variational approach to rare event simulation using least-squares regression

Abstract

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.

28 pages, 7 figures

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• Solving high-dimensional parabolic PDEs using the tensor train format
• Double-Loop Importance Sampling for McKean--Vlasov Stochastic Differential Equation
• Learning-Based Importance Sampling via Stochastic Optimal Control for Stochastic Reaction Networks
• Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics
• Nonasymptotic bounds for suboptimal importance sampling