Global Optimality in Bivariate Gradient-based DAG Learning
Chang Deng, Kevin Bello, Pradeep Kumar Ravikumar, Bryon Aragam
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.
BibTeX
@inproceedings{
deng2023global,
title={Global Optimality in Bivariate Gradient-based {DAG} Learning},
author={Chang Deng and Kevin Bello and Pradeep Kumar Ravikumar and Bryon Aragam},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=5MG5C5aS6m}
}