# A Neural Network Approach Applied to Multi-Agent Optimal Control

arXiv: https://arxiv.org/abs/2011.04757 · HTML: https://mlsanity.com/paper/2011.04757/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 14 of 14)

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- [End-to-End Training of High-Dimensional Optimal Control with Implicit Hamiltonians via Jacobian-Free Backpropagation](https://mlsanity.com/paper/2510.00359/) (2025)
- [Scalable Back-Propagation-Free Training of Optical Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.12384/) (2025)
- [PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning](https://mlsanity.com/paper/2309.15139/) (2023)
- [On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians](https://mlsanity.com/paper/2602.00921/) (2026)
- [Learning Control Policies of Hodgkin-Huxley Neuronal Dynamics](https://mlsanity.com/paper/2311.07563/) (2023)
- [Stability-Preserving Online Adaptation of Neural Closed-loop Maps](https://mlsanity.com/paper/2603.22469/) (2026)
- [End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers](https://mlsanity.com/paper/2607.20674/) (2026)

## Abstract (arXiv)

We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent control problems with obstacle and collision avoidance. These problems immediately become high-dimensional, even for moderate phase-space dimensions per agent. Our approach fuses the Pontryagin Maximum Principle and Hamilton-Jacobi-Bellman (HJB) approaches and parameterizes the value function with a neural network. Our approach yields controls in a feedback form for quick calculation and robustness to moderate disturbances to the system. We train our model using the objective function and optimality conditions of the control problem. Therefore, our training algorithm neither involves a data generation phase nor solutions from another algorithm. Our model uses empirically effective HJB penalizers for efficient training. By training on a distribution of initial states, we ensure the controls' optimality is achieved on a large portion of the state-space. Our approach is grid-free and scales efficiently to dimensions where grids become impractical or infeasible. We demonstrate our approach's effectiveness on a 150-dimensional multi-agent problem with obstacles.