Path signatures have been proposed as a powerful representation of paths that efficiently captures the path’s analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor products. Signatures have recently been widely adopted in machine learning problems for time series analysis. In this work we establish connections between value functions typically used in optimal control and intriguing properties of path signatures.

Encouraged by the remarkable achievements of language and vision foundation models, developing generalist robotic agents through imitation learning, using large demonstration datasets, has become a prominent area of interest in robot learning. The efficacy of imitation learning is heavily reliant on the quantity and quality of the demonstration datasets. In this study, we aim to scale up demonstrations in a data-efficient way to facilitate the learning of generalist robotic agents.