Switched diffusion processes for non-convex optimization and saddle points search

We introduce and investigate stochastic processes designed to find local minimizers and saddle points of non-convex functions, exploring the landscape more efficiently than the standard noisy gradient descent. The processes switch between two behaviours, a noisy gradient descent and a noisy saddle point search. It is proven to be well-defined and to converge to a stationary distribution in the long time. Numerical experiments are provided on low-dimensional toy models and for Lennard-Jones clusters.