Learning Time-Varying Directed Graphs via Convex TV-Regularized Optimization and DAG Projection

Continuous optimization methods for learning directed acyclic graphs (DAGs) have made progress in structure learning. However, they face two key limitations: (1) they assume a single, stationary graph structure across all observations, and (2) their nested nonconvex optimization with matrix exponential evaluations scales inefficiently as the number of variables grows—a bottleneck in high-dimensional applications. To address these limitations, we propose DACORD: DAG via Convex Optimization with Regime Detection, a two-stage method for learning time-varying DAGs. We utilize the insight that for models with a fixed feature map, acyclicity is the core source of nonconvexity in score-based DAG learning. Stage 1 jointly estimates window-specific coefficients by solving a convex regression problem with sparsity and total variation regularization. A single-loop primal–dual algorithm solves this problem, and changes in the estimated coefficients provide candidate regime boundaries. Stage 2 constructs a DAG for each estimated regime using greedy ordering and back-edge removal. Extensive experiments show that, at $d=200$ with $R=10$ regimes, DACORD completes in under 34 seconds with less than 1GB of GPU memory, whereas several existing methods either time out or fail numerically, and the completed baselines achieve lower precision and F1. Across completed comparable settings including the DREAM4 dataset, DACORD achieves the highest precision and F1 at high dimensional situation.