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Recently, a new class of non-convex optimization problems motivated by thestatistical problem of learning an acyclic directed graphical model from datahas attracted significant interest. While existing work uses standardfirst-order optimization schemes to solve this problem, proving the globaloptimality of such approaches has proven elusive. The difficulty lies in thefact that unlike other non-convex problems in the literature, this problem isnot "benign", and possesses multiple spurious solutions that standardapproaches can easily get trapped in. In this paper, we prove that a simplepath-following optimization scheme globally converges to the global minimum ofthe population loss in the bivariate setting.

Global Optimality in Bivariate Gradient-based DAG Learning