Global Optimality in Bivariate Gradient-based DAG Learning

Chang Deng, Kevin Bello, Pradeep Kumar Ravikumar, Bryon Aragam

Keywords: global optimization, nonconvex optimization, graphical models, directed acyclic graphs, structure learning

TL;DR: We prove that a simple path-following optimization scheme globally converges to the global minimum of the population loss in the bivariate setting of DAG Learning.

Abstract: Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order optimization schemes to solve this problem, proving the global optimality of such approaches has proven elusive. The difficulty lies in the fact that unlike other non-convex problems in the literature, this problem is not "benign", and possesses multiple spurious solutions that standard approaches can easily get trapped in. In this paper, we prove that a simple path-following optimization scheme globally converges to the global minimum of the population loss in the bivariate setting.

Submission Number: 16