Dexterous Skill Discovery via Topology-Aware Wasserstein Dependency

Dexterous object manipulation remains a fundamental challenge in robotics, typically requiring intensive supervision through explicit rewards, goals, or demonstrations. While unsupervised reinforcement learning (RL) holds the promise of discovering dexterous skills, state-of-the-art metric-aware methods have yet to be successfully applied to complex, high-dimensional manipulators like multi-fingered hands. We argue that this limitation stems from two key factors: existing methods lack the necessary inductive biases to prioritize object interaction over agent motion, and they fail to respect the non-Euclidean topology of object configuration space $\mathrm{SE}(3)$. To address these limitations, we propose a novel Wasserstein dependency measure between skills and object motions, formulated in the Lie algebra $\mathfrak{se}(3)$. Our approach, Topology-Aware SKill discovery (TASK), enables the discovery of fundamental manipulation skills—such as multi-axial object translation and rotation—without manual supervision. Across a range of embodiments, including non-prehensile and multi-fingered hands, our method learns dexterous behaviors where previous approaches fail, marking a significant step toward autonomous robotic dexterity.