Diversity You Can Actually Measure: A Fast, Model-Free Diversity Metric for Robotics Datasets

2026-03-12

AI Summary

This work addresses the challenge of measuring diversity in high-dimensional trajectory data from robotic imitation learning, which is hindered by variable lengths and complex structures. The authors propose the first fully model-agnostic diversity metric that requires neither policy nor environment interaction, by combining signature transforms with kernel methods and defining Shannon and von Neumann entropies based on the Gram matrix of the signature kernel. Building upon this metric, they introduce FAKTUAL, an efficient data selection algorithm that chooses a trajectory subset maximizing entropy under a given budget. Evaluated on RoboMimic, MetaWorld, and four real-world manipulation tasks, FAKTUAL substantially outperforms random sampling in improving downstream task success rates while incurring significantly lower computational overhead than existing approaches.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Robotics datasets for imitation learning typically consist of long-horizon trajectories of different lengths over states, actions, and high-dimensional observations (e.g., RGB video), making it non-trivial to quantify diversity in a way that respects the underlying trajectory structure and geometry. We extend Shannon and von Neumann entropy to this setting by defining signature transform-based entropy on the Gram matrix of a signature kernel over demonstrations, yielding entropy and diversity metrics that operate directly on the demonstration dataset. Building on these metrics, we study how dataset diversity affects generalization performance in robot imitation learning and propose a simple, model-free way to curate diverse demonstrations. We introduce FAKTUAL (FAst trajectory Kernel enTropy cUration for imitation Learning), a data curation algorithm that selects a subset of demonstrations maximizing entropy given a subset-size budget. FAKTUAL is fully model-free, requires no access to the imitation policy or rollouts, and adds negligible overhead relative to policy training. We evaluate our approach on image and state-based RoboMimic and MetaWorld benchmarks, as well as four real-world manipulation tasks. Across tasks and architectures, diversity-aware curation with FAKTUAL consistently improves downstream success rates over random selection, while being substantially more computationally efficient compared to recent robot data curation methods. Our results suggest that the entropy of demonstration datasets is a practical tool for understanding and improving dataset diversity in robot imitation learning.

Problem

• diversity
• robotics datasets
• imitation learning
• trajectory structure
• entropy

Innovation

• signature kernel
• trajectory entropy
• model-free curation
• imitation learning
• dataset diversity