  We reformulate a class of non-linear stochastic optimal control problems
introduced by Todorov (2007) as a Kullback-Leibler (KL) minimization problem.
As a result, the optimal control computation reduces to an inference
computation and approximate inference methods can be applied to efficiently
compute approximate optimal controls. We show how this KL control theory
contains the path integral control method as a special case. We provide an
example of a block stacking task and a multi-agent cooperative game where we
demonstrate how approximate inference can be successfully applied to instances
that are too complex for exact computation. We discuss the relation of the KL
control approach to other inference approaches to control.
