  Propagating state distributions through a generic, uncertain nonlinear
dynamical model is known to be intractable and usually begets numerical or
analytical approximations. We introduce a method for state prediction, called
the Expansion-Compression Unscented Transform, and use it to solve a class of
online policy optimization problems. Our proposed algorithm propagates a finite
number of sigma points through a state-dependent distribution, which dictates
an increase in the number of sigma points at each time step to represent the
resulting distribution; this is what we call the expansion operation. To keep
the algorithm scalable, we augment the expansion operation with a compression
operation based on moment matching, thereby keeping the number of sigma points
constant across predictions over multiple time steps. Its performance is
empirically shown to be comparable to Monte Carlo but at a much lower
computational cost. Under state and control input constraints, the state
prediction is subsequently used in tandem with a proposed variant of
constrained gradient-descent for online update of policy parameters in a
receding horizon fashion. The framework is implemented as a differentiable
computational graph for policy training. We showcase our framework for a
quadrotor stabilization task as part of a benchmark comparison in
safe-control-gym and for optimizing the parameters of a Control Barrier
Function based controller in a leader-follower problem.
