# Learning Control Admissibility Models with Graph Neural Networks for Multi-Agent Navigation

arXiv: https://arxiv.org/abs/2210.09378 · HTML: https://mlsanity.com/paper/2210.09378/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 53 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1803.11485/) (2018)
- [Learning to Communicate with Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1605.06676/) (2016)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [A Survey of Autonomous Driving: Common Practices and Emerging Technologies](https://mlsanity.com/paper/1906.05113/) (2019)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Inverse Reward Design](https://mlsanity.com/paper/1711.02827/) (2017)
- [Multi-Agent Pathfinding: Definitions, Variants, and Benchmarks](https://mlsanity.com/paper/1906.08291/) (2019)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [PRIMAL: Pathfinding via Reinforcement and Imitation Multi-Agent Learning](https://mlsanity.com/paper/1809.03531/) (2018)
- [Graph Neural Networks for Decentralized Multi-Robot Path Planning](https://mlsanity.com/paper/1912.06095/) (2019)
- [Searching with Consistent Prioritization for Multi-Agent Path Finding](https://mlsanity.com/paper/1812.06356/) (2018)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [PIC: Permutation Invariant Critic for Multi-Agent Deep Reinforcement Learning](https://mlsanity.com/paper/1911.00025/) (2019)
- [Message-Aware Graph Attention Networks for Large-Scale Multi-Robot Path Planning](https://mlsanity.com/paper/2011.13219/) (2020)
- [Graph Policy Gradients for Large Scale Robot Control](https://mlsanity.com/paper/1907.03822/) (2019)
- [GLAS: Global-to-Local Safe Autonomy Synthesis for Multi-Robot Motion Planning with End-to-End Learning](https://mlsanity.com/paper/2002.11807/) (2020)
- [Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions](https://mlsanity.com/paper/2003.02992/) (2020)
- [Multi-Robot Coverage and Exploration using Spatial Graph Neural Networks](https://mlsanity.com/paper/2011.01119/) (2020)
- [Graph Neural Networks for Decentralized Multi-Robot Submodular Action Selection](https://mlsanity.com/paper/2105.08601/) (2021)
- [Graph Neural Networks for Motion Planning](https://mlsanity.com/paper/2006.06248/) (2020)
- [Probabilistic and Distributed Control of a Large-Scale Swarm of Autonomous Agents](https://mlsanity.com/paper/1403.4134/) (2014)

## Built on by (most cited first, 8 of 8)

- [Graphs Meet AI Agents: Taxonomy, Progress, and Future Opportunities](https://mlsanity.com/paper/2506.18019/) (2025)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [Co-Optimizing Reconfigurable Environments and Policies for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2403.14583/) (2024)
- [Accelerating Multi-Agent Planning Using Graph Transformers with Bounded Suboptimality](https://mlsanity.com/paper/2301.08451/) (2023)
- [Estimating Control Barriers from Offline Data](https://mlsanity.com/paper/2503.10641/) (2025)
- [Controllable Motion Generation via Diffusion Modal Coupling](https://mlsanity.com/paper/2503.02353/) (2025)
- [Reliable and Efficient Multi-Agent Coordination via Graph Neural Network Variational Autoencoders](https://mlsanity.com/paper/2503.02954/) (2025)
- [CollisionGAT: Controller-Agnostic One-Step Collision Screening for Multi-Agent Motion](https://mlsanity.com/paper/2609.32783/) (2026)

## Abstract (arXiv)

Deep reinforcement learning in continuous domains focuses on learning control policies that map states to distributions over actions that ideally concentrate on the optimal choices in each step. In multi-agent navigation problems, the optimal actions depend heavily on the agents' density. Their interaction patterns grow exponentially with respect to such density, making it hard for learning-based methods to generalize. We propose to switch the learning objectives from predicting the optimal actions to predicting sets of admissible actions, which we call control admissibility models (CAMs), such that they can be easily composed and used for online inference for an arbitrary number of agents. We design CAMs using graph neural networks and develop training methods that optimize the CAMs in the standard model-free setting, with the additional benefit of eliminating the need for reward engineering typically required to balance collision avoidance and goal-reaching requirements. We evaluate the proposed approach in multi-agent navigation environments. We show that the CAM models can be trained in environments with only a few agents and be easily composed for deployment in dense environments with hundreds of agents, achieving better performance than state-of-the-art methods.