# MAD-PINN: A Decentralized Physics-Informed Machine Learning Framework for Safe and Optimal Multi-Agent Control

arXiv: https://arxiv.org/abs/2509.23960 · HTML: https://mlsanity.com/paper/2509.23960/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 20 of 20)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Scalable Multi-Agent Reinforcement Learning through Intelligent Information Aggregation](https://mlsanity.com/paper/2211.02127/) (2022)
- [Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Prediction](https://mlsanity.com/paper/2312.08604/) (2023)
- [A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems](https://mlsanity.com/paper/2502.11057/) (2025)
- [On Safety and Liveness Filtering Using Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2312.15347/) (2023)
- [Learning a Formally Verified Control Barrier Function in Stochastic Environment](https://mlsanity.com/paper/2403.19332/) (2024)
- [Exact Imposition of Safety Boundary Conditions in Neural Reachable Tubes](https://mlsanity.com/paper/2404.00814/) (2024)
- [Semi-Supervised Safe Visuomotor Policy Synthesis using Barrier Certificates](https://mlsanity.com/paper/2409.12616/) (2024)
- [Resolving Conflicting Constraints in Multi-Agent Reinforcement Learning with Layered Safety](https://mlsanity.com/paper/2505.02293/) (2025)
- [Solving Multi-Agent Safe Optimal Control with Distributed Epigraph Form MARL](https://mlsanity.com/paper/2504.15425/) (2025)
- [CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functions](https://mlsanity.com/paper/2503.17395/) (2025)
- [Multi-Agent Path Integral Control for Interaction-Aware Motion Planning in Urban Canals](https://mlsanity.com/paper/2302.06547/) (2023)
- [Multi-Agent Reinforcement Learning in Intelligent Transportation Systems: A Comprehensive Survey](https://mlsanity.com/paper/2508.20315/) (2025)

## Abstract (arXiv)

Co-optimizing safety and performance in large-scale multi-agent systems remains a fundamental challenge. Existing approaches based on multi-agent reinforcement learning (MARL), safety filtering, or Model Predictive Control (MPC) either lack strict safety guarantees, suffer from conservatism, or fail to scale effectively. We propose MAD-PINN, a decentralized physics-informed machine learning framework for solving the multi-agent state-constrained optimal control problem (MASC-OCP). Our method leverages an epigraph-based reformulation of SC-OCP to simultaneously capture performance and safety, and approximates its solution via a physics-informed neural network. Scalability is achieved by training the SC-OCP value function on reduced-agent systems and deploying them in a decentralized fashion, where each agent relies only on local observations of its neighbours for decision-making. To further enhance safety and efficiency, we introduce an Hamilton-Jacobi (HJ) reachability-based neighbour selection strategy to prioritize safety-critical interactions, and a receding-horizon policy execution scheme that adapts to dynamic interactions while reducing computational burden. Experiments on multi-agent navigation tasks demonstrate that MAD-PINN achieves superior safety-performance trade-offs, maintains scalability as the number of agents grows, and consistently outperforms state-of-the-art baselines.