While the topic of nonlinear stochastic control has been traditionally studied within control theory and applied mathematics, over the past 10-15 years there has been an increasing interest by researchers in the machine learning, statistical physics and robotics communities to expand nonlinear stochastic optimal control in terms of theoretical generalizations and algorithms. The main motivation for this increasing interest is the ability to solve stochastic optimal control problems with forward sampling of Stochastic Differential Equations (SDEs). There has been few approaches in the literature on this topic under the names of path integral control, Kullback-Leibler control or linearly solvable optimal control.
In this talk, in the first half I will present a unified view of the aforementioned approaches on stochastic control theory and show applications to autonomous systems and robotics. On the second half, I will present ongoing research on generalizations of stochastic control and show new algorithms for trajectory optimization based on non-parametric regression methods.