Branch-Price-and-Cut for Causal Discovery

We show how to extend the integer programming (IP) approach to score-based causal discovery by including pricing. Pricing allows the addition of new IP variables during solving, rather than requiring them all to be present initially. The dual values of acyclicity constraints allow this addition to be done in a principled way. We have extended the GOBNILP algorithm to effect a branch-price-and-cut method for DAG learning. Empirical results show that implementing a delayed pricing approach can be beneficial. The current pricing algorithm in GOBNILP is slow, so further work on fast pricing is required.