# Distributed Control of Network Systems in the Space of Stabilizing Graph Neural Network Policies

arXiv: https://arxiv.org/abs/2512.18540 · HTML: https://mlsanity.com/paper/2512.18540/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 20 Dec 2025.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 16 of 16)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Scalable Multi-Agent Reinforcement Learning through Intelligent Information Aggregation](https://mlsanity.com/paper/2211.02127/) (2022)
- [GCBF+: A Neural Graph Control Barrier Function Framework for Distributed Safe Multi-Agent Control](https://mlsanity.com/paper/2401.14554/) (2024)
- [Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System](https://mlsanity.com/paper/2112.04219/) (2021)
- [Distributed Linear-Quadratic Control with Graph Neural Networks](https://mlsanity.com/paper/2103.08417/) (2021)
- [Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach](https://mlsanity.com/paper/2112.09046/) (2021)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [On Safety and Liveness Filtering Using Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2312.15347/) (2023)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2206.01704/) (2022)
- [Optimal distributed control with stability guarantees by training a network of neural closed-loop maps](https://mlsanity.com/paper/2404.02820/) (2024)
- [MAD: A Magnitude And Direction Policy Parametrization for Stability Constrained Reinforcement Learning](https://mlsanity.com/paper/2504.02565/) (2025)

## Abstract (arXiv)

We study distributed control of networked systems through reinforcement learning, where neural policies must be simultaneously scalable, expressive and stabilizing. We introduce a policy parameterization that embeds Graph Neural Networks (GNNs) into a Youla-like magnitude-direction parameterization, yielding distributed stochastic controllers that guarantee network-level closed-loop stability by design. The magnitude is implemented as a stable operator consisting of a GNN acting on disturbance feedback, while the direction is a GNN acting on local observations. We prove robustness of the policy to perturbations in both the graph topology and model parameters. Numerical experiments validate the effectiveness of the proposed approach.