  A common pipeline in learning-based control is to iteratively estimate a
model of system dynamics, and apply a trajectory optimization algorithm -
e.g.~$\mathtt{iLQR}$ - on the learned model to minimize a target cost. This
paper conducts a rigorous analysis of a simplified variant of this strategy for
general nonlinear systems. We analyze an algorithm which iterates between
estimating local linear models of nonlinear system dynamics and performing
$\mathtt{iLQR}$-like policy updates. We demonstrate that this algorithm attains
sample complexity polynomial in relevant problem parameters, and, by
synthesizing locally stabilizing gains, overcomes exponential dependence in
problem horizon. Experimental results validate the performance of our
algorithm, and compare to natural deep-learning baselines.
