Cross-entropy (CE) minimization is a versatile Monte Carlo method for combinatorial optimization and sampling of rare events, which goes back to work by Reuven Rubinstein and co-workers. I will report on recent algorithmic extensions of the CE method to diffusions that can be used to design efficient importance sampling strategies for computing the rare events statistics of equilibrated systems. The approach is based on a Legendre-type duality between path functionals of diffusion processes associated with certain sampling and control problems that can be reformulated in terms of CE minimization. The method will be illustrated with several numerical examples and discussed along with algorithmic issues and possible extensions of the method to high-dimensional multiscale systems. Related approaches based on large deviation asymptotics will be discussed during the talk.
This is joint work with Wei Zhang and Christof Schütte.