Learning latent costs of transitions on graphs from trajectories demonstrations under various contextual features is challenging but useful for path planning. Yet, existing methods either oversimplify cost assumptions or scale poorly with the number of observed trajectories. This paper introduces DataSP, a differentiable all-to-all shortest path algorithm to facilitate learning latent costs from trajectories. It allows to learn from a large number of trajectories in each learning step without additional computation. Complex latent cost functions from contextual features can be represented in the algorithm through a neural network approximation. We further propose a method to sample paths from DataSP in order to reconstruct/mimic observed paths' distributions. We prove that the inferred distribution follows the maximum entropy principle. We show that DataSP outperforms state-of-the-art differentiable combinatorial solver and classical machine learning approaches in predicting paths on graphs.

翻译：在各种上下文特征下，从轨迹演示中学习图上的隐式转移成本具有挑战性，但对路径规划非常有用。然而，现有方法要么过度简化成本假设，要么在观测轨迹数量增加时扩展性较差。本文提出了DataSP，一种可微分的全对最短路径算法，以促进从轨迹中学习隐式成本。该算法允许在每个学习步骤中从大量轨迹中学习，而无需额外计算。通过神经网络近似，算法可以表示来自上下文特征的复杂隐式成本函数。我们进一步提出了一种从DataSP中采样路径的方法，以重建/模拟观测路径的分布。我们证明了推断的分布遵循最大熵原理。实验表明，在图路径预测任务上，DataSP优于当前最先进的可微分组合求解器及经典机器学习方法。