Geometry-aware Policy Imitation

2025-10-09

AI Summary

Conventional imitation learning treats demonstrations as discrete state-action pairs, limiting expressiveness and generalization. Method: We propose a geometric curve perspective—modeling expert demonstrations as continuous geometric curves—and construct a distance field to generate dual control flows: forward progression and attraction forces. This yields an interpretable, non-parametric vector field policy. Our approach decouples metric learning from policy generation, enabling multimodal demonstration fusion and incremental composition; it integrates differential geometry with motion planning to unify policy representation across low-dimensional state spaces and high-dimensional perceptual inputs. Contribution/Results: Evaluated in simulation and on real robots, our method achieves higher success rates than diffusion-based baselines, with 20× faster inference, significantly lower memory footprint, and superior robustness to environmental disturbances.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Search and Optimization: Learning to Search
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

Problem

• Treats demonstrations as geometric curves for imitation learning
• Derives distance fields to create progression and attraction control primitives
• Decouples metric learning from policy synthesis for modular adaptation

Innovation

• Treats demonstrations as geometric curves
• Derives progression and attraction control primitives
• Decouples metric learning from policy synthesis