  "Monkey see monkey do" is an age-old adage, referring to na\"ive imitation
without a deep understanding of a system's underlying mechanics. Indeed, if a
demonstrator has access to information unavailable to the imitator (monkey),
such as a different set of sensors, then no matter how perfectly the imitator
models its perceived environment (See), attempting to reproduce the
demonstrator's behavior (Do) can lead to poor outcomes. Imitation learning in
the presence of a mismatch between demonstrator and imitator has been studied
in the literature under the rubric of causal imitation learning (Zhang et al.,
2020), but existing solutions are limited to single-stage decision-making. This
paper investigates the problem of causal imitation learning in sequential
settings, where the imitator must make multiple decisions per episode. We
develop a graphical criterion that is necessary and sufficient for determining
the feasibility of causal imitation, providing conditions when an imitator can
match a demonstrator's performance despite differing capabilities. Finally, we
provide an efficient algorithm for determining imitability and corroborate our
theory with simulations.
