  Discrete-time stochastic optimal control remains a challenging problem for
general, nonlinear systems under significant uncertainty, with practical
solvers typically relying on the certainty equivalence assumption, replanning
and/or extensive regularization. Control as inference is an approach that
frames stochastic control as an equivalent inference problem, and has
demonstrated desirable qualities over existing methods, namely in exploration
and regularization. We look specifically at the input inference for control
(i2c) algorithm, and derive three key characteristics that enable advanced
trajectory optimization: An `expert' linear Gaussian controller that combines
the benefits of open-loop optima and closed-loop variance reduction when
optimizing for nonlinear systems, inherent adaptive risk sensitivity from the
inference formulation, and covariance control functionality with only a minor
algorithmic adjustment.
