$ψ$DAG: Projected Stochastic Approximation Iteration for DAG Structure Learning

Klea Ziu; Slavomír Hanzely; Loka Li; Kun Zhang; Martin Takáč; Dmitry Kamzolov

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arXiv · 2410.23862

$ψ$DAG: Projected Stochastic Approximation Iteration for DAG Structure Learning

Klea Ziu·Slavomír Hanzely·Loka Li·Kun Zhang·Martin Takáč·Dmitry Kamzolov

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Abstract

Learning the structure of Directed Acyclic Graphs (DAGs) presents a significant challenge due to the vast combinatorial search space of possible graphs, which scales exponentially with the number of nodes. Recent advancements have redefined this problem as a continuous optimization task by incorporating differentiable acyclicity constraints. These methods commonly rely on algebraic characterizations of DAGs, such as matrix exponentials, to enable the use of gradient-based optimization techniques. Despite these innovations, existing methods often face optimization difficulties due to the highly non-convex nature of DAG constraints and the per-iteration computational complexity. In this work, we present a novel framework for learning DAGs, employing a Stochastic Approximation approach integrated with Stochastic Gradient Descent (SGD)-based optimization techniques. Our framework introduces new projection methods tailored to efficiently enforce DAG constraints, ensuring that the algorithm converges to a feasible local minimum. With its low iteration complexity, the proposed method is well-suited for handling large-scale problems with improved computational efficiency. We demonstrate the effectiveness and scalability of our framework through comprehensive experimental evaluations, which confirm its superior performance across various settings.

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BibTeX RIS

Klea Ziu, Slavomír Hanzely, Loka Li, Kun Zhang, Martin Takáč, Dmitry Kamzolov. 2024-10-31. $ψ$DAG: Projected Stochastic Approximation Iteration for DAG Structure Learning. https://arxiv.org/abs/2410.23862

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