  While the identification of nonlinear dynamical systems is a fundamental
building block of model-based reinforcement learning and feedback control, its
sample complexity is only understood for systems that either have discrete
states and actions or for systems that can be identified from data generated by
i.i.d. random inputs. Nonetheless, many interesting dynamical systems have
continuous states and actions and can only be identified through a judicious
choice of inputs. Motivated by practical settings, we study a class of
nonlinear dynamical systems whose state transitions depend linearly on a known
feature embedding of state-action pairs. To estimate such systems in finite
time identification methods must explore all directions in feature space. We
propose an active learning approach that achieves this by repeating three
steps: trajectory planning, trajectory tracking, and re-estimation of the
system from all available data. We show that our method estimates nonlinear
dynamical systems at a parametric rate, similar to the statistical rate of
standard linear regression.
