  Structural learning, which aims to learn directed acyclic graphs (DAGs) from
observational data, is foundational to causal reasoning and scientific
discovery. Recent advancements formulate structural learning into a continuous
optimization problem; however, DAG learning remains a highly non-convex
problem, and there has not been much work on leveraging well-developed convex
optimization techniques for causal structural learning. We fill this gap by
proposing a data-adaptive linear approach for causal structural learning from
time series data, which can be conveniently cast into a convex optimization
problem using a recently developed monotone operator variational inequality
(VI) formulation. Furthermore, we establish non-asymptotic recovery guarantee
of the VI-based approach and show the superior performance of our proposed
method on structure recovery over existing methods via extensive numerical
experiments.
