Optimizing NOTEARS Objectives via Topological Swaps

• URL: http://arxiv.org/abs/2305.17277v1
• Date: Fri, 26 May 2023 21:49:37 GMT
• Title: Optimizing NOTEARS Objectives via Topological Swaps
• Authors: Chang Deng, Kevin Bello, Bryon Aragam, Pradeep Ravikumar
• Abstract summary: In this paper, we develop an effective method for a set of candidate algorithms. At the inner level, given a subject, we utilize off-the-the-art constraints. The proposed method significantly improves the score of other algorithms.
• Score: 41.18829644248979
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

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