Breaking the Scalability Barrier in Constrained Graph-Based Networked Control via Decision-Focused Learning

Many real-world systems can be modeled as graphs, where nodes store and consume entities, actively produce them, or have them emerge naturally, and edges transport them between nodes. This paper studies the networked control problem on such large-scale systems, aiming to decide production and transportation over time to maximize long-term profits, subject to node or edge capacity constraints. Existing SOTAs either fail to guarantee feasibility or cannot scale to large-scale systems. We propose a two-stage policy that integrates a constrained optimization layer after a neural network to explicitly enforce constraints and ensure feasibility. By leveraging the problem structure to obtain expert actions and designing a decision-focused and differentiable loss to enable imitation learning, our method significantly improves efficiency and scalability. In small-scale systems with action dimensions in the order of 10, our method achieves 60x sample efficiency over SOTAs on average. In large-scale systems with action dimensions ranging from 100 to 100000, where SOTAs fail to train, our method converges quickly and outperforms non-learning-based baselines significantly.