  To date, most directed acyclic graphs (DAGs) structure learning approaches
require data to be stored in a central server. However, due to the
consideration of privacy protection, data owners gradually refuse to share
their personalized raw data to avoid private information leakage, making this
task more troublesome by cutting off the first step. Thus, a puzzle arises:
\textit{how do we discover the underlying DAG structure from decentralized
data?} In this paper, focusing on the additive noise models (ANMs) assumption
of data generation, we take the first step in developing a gradient-based
learning framework named FedDAG, which can learn the DAG structure without
directly touching the local data and also can naturally handle the data
heterogeneity. Our method benefits from a two-level structure of each local
model. The first level structure learns the edges and directions of the graph
and communicates with the server to get the model information from other
clients during the learning procedure, while the second level structure
approximates the mechanisms among variables and personally updates on its own
data to accommodate the data heterogeneity. Moreover, FedDAG formulates the
overall learning task as a continuous optimization problem by taking advantage
of an equality acyclicity constraint, which can be solved by gradient descent
methods to boost the searching efficiency. Extensive experiments on both
synthetic and real-world datasets verify the efficacy of the proposed method.
