A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding

Understand

We propose a neural network approach that yields approximate solutions for high-dimensional optimal control problems and demonstrate its effectiveness using examples from multi-agent path finding.

• Our approach yields controls in a feedback form, where the policy function is given by a neural network (NN).
• Specifically, we fuse the Hamilton-Jacobi-Bellman (HJB) and Pontryagin Maximum Principle (PMP) approaches by parameterizing the value function with an NN.
• Our approach enables us to obtain approximately optimal controls in real-time without having to solve an optimization problem.