To find the shortest paths for all pairs on manifolds with infinitesimally defined metrics, we introduce a framework to generate them by predicting midpoints recursively. To learn midpoint prediction, we propose an actor-critic approach. We prove the soundness of our approach and show experimentally that the proposed method outperforms existing methods on several planning tasks, including path planning for agents with complex kinematics and motion planning for multi-degree-of-freedom robot arms.

翻译：为求解在无穷小度量定义流形上所有点对之间的最短路径，我们提出一种通过递归预测中点来生成这些路径的框架。为学习中点预测，我们提出一种actor-critic方法。我们证明了该方法的合理性，并通过实验表明，所提方法在多项规划任务中优于现有方法，包括具有复杂运动学智能体的路径规划以及多自由度机械臂的运动规划。