  We propose Taylor Series Imitation Learning (TaSIL), a simple augmentation to
standard behavior cloning losses in the context of continuous control. TaSIL
penalizes deviations in the higher-order Taylor series terms between the
learned and expert policies. We show that experts satisfying a notion of
$\textit{incremental input-to-state stability}$ are easy to learn, in the sense
that a small TaSIL-augmented imitation loss over expert trajectories guarantees
a small imitation loss over trajectories generated by the learned policy. We
provide sample-complexity bounds for TaSIL that scale as
$\tilde{\mathcal{O}}(1/n)$ in the realizable setting, for $n$ the number of
expert demonstrations. Finally, we demonstrate experimentally the relationship
between the robustness of the expert policy and the order of Taylor expansion
required in TaSIL, and compare standard Behavior Cloning, DART, and DAgger with
TaSIL-loss-augmented variants. In all cases, we show significant improvement
over baselines across a variety of MuJoCo tasks.
