Fast Non-Parametric Heteroscedastic Imitation Learning With Geometric Priors

2026-10-06

AI Summary

This study addresses the lack of geometric awareness, unreliable uncertainty estimation, and the need for retraining when generalizing to novel scenarios in robot imitation learning. To overcome these limitations, this work proposes a nonparametric kernel method that incorporates manifold geometric priors. By supporting non-separable diagonal kernels to model uncertainty correlations across degrees of freedom, the approach enables heteroscedastic probabilistic policy learning. Furthermore, its optimization formulation accommodates manifold-valued inputs and outputs alongside task parameterization, facilitating rapid adaptation to new scenarios without retraining. Experimental results demonstrate that trajectory updates require less than three milliseconds. The method’s high data efficiency and reliable adaptability are further validated through real-world robotic manipulation and shared-control tasks.

Abstract

When learning probabilistic policies from human demonstrations, data-efficient learning and fast adaptations to new scenarios are key requirements. One popular way to achieve intuitive and reliable adaptations is through non-parametric, typically kernel-based, methods. However, existing solutions either fail to account for the geometry of manifolds common in robotics, limiting data efficiency, or, when geometry-aware, provide unreliable uncertainty estimates or require retraining to adapt. We propose a non-parametric approach leveraging geometric priors in scenarios of data scarcity and heteroscedastic uncertainties for probabilistic modeling. We utilize the method to formulate policies based on time or robot state, where non-separable diagonal kernels allow capturing uncertainty relations between degrees of freedom for same-sized in- and outputs. Fast updates, requiring less than 3 ms for a trajectory involving both position and orientation are possible through an optimized formulation. Our approach supports both manifold-valued input and manifold-valued output with large orientation changes. Using task parameterization, adaptation to different object poses is easily possible. We evaluate the approach on a set of toy examples and on real robot manipulation tasks both in autonomous execution and in shared control scenarios.

Problem

• Imitation Learning
• Non-Parametric Methods
• Heteroscedastic Uncertainty
• Manifold Geometry
• Data Efficiency

Innovation

• Non-Parametric Imitation Learning
• Geometric Priors
• Heteroscedastic Uncertainty
• Manifold-valued Kernels
• Task Parameterization