  Drawbacks of ignoring the causal mechanisms when performing imitation
learning have recently been acknowledged. Several approaches both to assess the
feasibility of imitation and to circumvent causal confounding and causal
misspecifications have been proposed in the literature. However, the potential
benefits of the incorporation of additional information about the underlying
causal structure are left unexplored. An example of such overlooked information
is context-specific independence (CSI), i.e., independence that holds only in
certain contexts. We consider the problem of causal imitation learning when CSI
relations are known. We prove that the decision problem pertaining to the
feasibility of imitation in this setting is NP-hard. Further, we provide a
necessary graphical criterion for imitation learning under CSI and show that
under a structural assumption, this criterion is also sufficient. Finally, we
propose a sound algorithmic approach for causal imitation learning which takes
both CSI relations and data into account.
