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arXiv · 2306.17378

Global Optimality in Bivariate Gradient-based DAG Learning

Chang Deng·Kevin Bello·Bryon Aragam·Pradeep Ravikumar
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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.

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Chang Deng, Kevin Bello, Bryon Aragam, Pradeep Ravikumar. 2023-06-30. Global Optimality in Bivariate Gradient-based DAG Learning. https://arxiv.org/abs/2306.17378

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