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

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

We propose a neural network (NN) approach that yields approximate solutions for high-dimensional optimal control (OC) problems and demonstrate its effectiveness using examples from multiagent path finding. Our approach yields control in a feedback form, where the policy function is given by an NN. In particular, 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 OCs in real time without having to solve an optimization problem. Once the policy function is trained, generating a control at a given space–time location takes milliseconds; in contrast, efficient nonlinear programming methods typically perform the same task in seconds. We train the NN offline using the objective function of the control problem and penalty terms that enforce the HJB equations. Therefore, our training algorithm does not involve data generated by another algorithm. By training on a distribution of initial states, we ensure the controls’ optimality on a large portion of the state space. Our grid-free approach scales efficiently to dimensions where grids become impractical or infeasible. We apply our approach to several multiagent collision-avoidance problems in up to 150 dimensions. Furthermore, we empirically observe that the number of parameters in our approach scales linearly with the dimension of the control problem, thereby mitigating the curse of dimensionality.

我们提出了一种神经网络（NN）方法，该方法可为高维最佳控制（OC）提供近似的解决方案，并使用多种路径的示例来证明其有效性，我们的方法以反馈形式产生控制。因此，我们的方法能够实时获得大约的OC，而不必解决策略功能。通过对初始状态的分布进行训练，涉及另一个算法，我们在状态空间的大部分方面的最佳性能有效地缩放到不可能的方法中，我们的方法是不切实际的。与控制问题的维度，从而减轻维数的曲线。