Sub-Goal Trees -- a Framework for Goal-Directed Trajectory Prediction and Optimization

TL;DR

This paper introduces sub-goal trees as a novel hierarchical trajectory representation for goal-directed AI tasks, improving prediction speed and accuracy in motion planning through recursive partitioning and dynamic programming.

Contribution

It proposes a new hierarchical sub-goal tree framework for trajectory prediction and optimization, offering faster computation and better modeling of trajectory variability.

Findings

Sub-goal trees outperform sequential models in trajectory prediction accuracy.

The framework enables exponential speed-up in trajectory prediction at test time.

New planning algorithms based on sub-goal trees improve motion planning performance.

Abstract

Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. In such problems, the way we choose to represent a trajectory underlies algorithms for trajectory prediction and optimization. Interestingly, most all prior work in imitation and reinforcement learning builds on a sequential trajectory representation -- calculating the next state in the trajectory given its predecessors. We propose a different perspective: a goal-conditioned trajectory can be represented by first selecting an intermediate state between start and goal, partitioning the trajectory into two. Then, recursively, predicting intermediate points on each sub-segment, until a complete trajectory is obtained. We call this representation a sub-goal tree, and building on it, we develop new methods for trajectory prediction, learning, and optimization. We show that in a supervised learning setting, sub-goal trees better account for trajectory variability, and can predict trajectories exponentially faster at test time by leveraging a concurrent computation. Then, for optimization, we derive a new dynamic programming equation for sub-goal trees, and use it to develop new planning and reinforcement learning algorithms. These algorithms, which are not based on the standard Bellman equation, naturally account for hierarchical sub-goal structure in a task. Empirical results on motion planning domains show that the sub-goal tree framework significantly improves both accuracy and prediction time.