Path integral control and state-dependent feedback

In this paper we address the problem of computing state-dependent feedback controls for path integral control problems. To this end we generalize the path integral control formula and utilize this to construct parametrized state-dependent feedback controllers. In addition, we show a relation between control and importance sampling: Better control, in terms of control cost, yields more efficient importance sampling, in terms of effective sample size. The optimal control provides a zero-variance estimate.