The Imitation Learning problem is usually mixed with RL, since Imitation Learning is a inclusive term(function-related) while RL is a principle-related term. So RL could serve as one kind of imitation learning. Paper of this could be seen at DeepMimic.
Imitation Learning, in its strict definition, is to learn a whole trajectory of action under expert demostrations, using whatever methods. The goal of imitation learning is to find a policy $\pi$
\[\hat{\pi} = \arg\min_{\pi \in \Pi} \mathbb{E}_{s \sim d_{\pi}}\left[\ell(s, \pi)\right]\]which minimizes the cost (surrogate cost, because we could not find the “true” value of cost $\mathbb{C}$)
