  Modern machine learning approaches excel in static settings where a large
amount of i.i.d. training data are available for a given task. In a dynamic
environment, though, an intelligent agent needs to be able to transfer
knowledge and re-use learned components across domains. It has been argued that
this may be possible through causal models, aiming to mirror the modularity of
the real world in terms of independent causal mechanisms. However, the true
causal structure underlying a given set of data is generally not identifiable,
so it is desirable to have means to quantify differences between models (e.g.,
between the ground truth and an estimate), on both the observational and
interventional level.
  In the present work, we introduce the Interventional Kullback-Leibler (IKL)
divergence to quantify both structural and distributional differences between
models based on a finite set of multi-environment distributions generated by
interventions from the ground truth. Since we generally cannot quantify all
differences between causal models for every finite set of interventional
distributions, we propose a sufficient condition on the intervention targets to
identify subsets of observed variables on which the models provably agree or
disagree.
