DataSP: A Differential All-to-All Shortest Path Algorithm for Learning Costs and Predicting Paths with Context

TL;DR

DataSP is a novel differentiable shortest path algorithm that efficiently learns complex latent costs from large trajectory datasets, enabling accurate path prediction and distribution reconstruction under various contextual features.

Contribution

It introduces a differentiable all-to-all shortest path algorithm capable of learning from many trajectories simultaneously using neural network approximations.

Findings

DataSP outperforms existing methods in path prediction accuracy.

It effectively models complex latent costs with neural networks.

The inferred path distribution adheres to the maximum entropy principle.

Abstract

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.