  Learning a causal directed acyclic graph from data is a challenging task that
involves solving a combinatorial problem for which the solution is not always
identifiable. A new line of work reformulates this problem as a continuous
constrained optimization one, which is solved via the augmented Lagrangian
method. However, most methods based on this idea do not make use of
interventional data, which can significantly alleviate identifiability issues.
This work constitutes a new step in this direction by proposing a
theoretically-grounded method based on neural networks that can leverage
interventional data. We illustrate the flexibility of the
continuous-constrained framework by taking advantage of expressive neural
architectures such as normalizing flows. We show that our approach compares
favorably to the state of the art in a variety of settings, including perfect
and imperfect interventions for which the targeted nodes may even be unknown.
