Reinforcement Learning for Global-Local Control of Dynamic Networks with Applications to Systemic Risk

Abstract

We propose a reinforcement learning framework for solving control problems on dynamic networks, where control decisions consist of a combination of graph-level (global) and node-level (local) actions. To exploit the underlying network structure in a policy-gradient algorithm, we introduce a message-passing neural network architecture with separate global and local policy heads. The architecture ensures that the resulting policies satisfy natural permutation symmetries and transparency constraints. Our main theoretical contribution is an analysis of the robustness and regularity properties of the proposed architecture. We derive explicit Lipschitz bounds with respect to both parameter and input perturbations and use these estimates to establish convergence guarantees for a projected policy-gradient algorithm. The resulting constants reveal how architectural choices and graph characteristics influence sensitivity to input perturbations and the convergence behavior of gradient-based optimization methods. As an application, we study the management of systemic risk in financial networks, where a regulator allocates capital interventions across interconnected institutions. Numerical experiments demonstrate that the proposed reinforcement learning architecture outperforms standard architectures based on feedforward neural networks while the learned policies fulfill desirable symmetry and transparency constraints. The algorithm scales to large networks and effectively combines global budget decisions with local allocation policies by exploiting the underlying graph structure.