Abstract
We present a reformulation of the stochastic optimal control problem in terms of KL divergence minimisation, not only providing a unifying perspective of previous approaches in this area, but also demonstrating that the formalism leads to novel practical approaches to the control problem. Speci?cally, a natural relaxation of the dual formulation gives rise to exact iterative solutions to the ?nite and in?nite horizon stochastic optimal control problem, while direct application of Bayesian inference methods yields instances of risk sensitive control.