  We propose ordering-based approaches for learning the maximal ancestral graph
(MAG) of a structural equation model (SEM) up to its Markov equivalence class
(MEC) in the presence of unobserved variables. Existing ordering-based methods
in the literature recover a graph through learning a causal order (c-order). We
advocate for a novel order called removable order (r-order) as they are
advantageous over c-orders for structure learning. This is because r-orders are
the minimizers of an appropriately defined optimization problem that could be
either solved exactly (using a reinforcement learning approach) or
approximately (using a hill-climbing search). Moreover, the r-orders (unlike
c-orders) are invariant among all the graphs in a MEC and include c-orders as a
subset. Given that set of r-orders is often significantly larger than the set
of c-orders, it is easier for the optimization problem to find an r-order
instead of a c-order. We evaluate the performance and the scalability of our
proposed approaches on both real-world and randomly generated networks.
