Data-dependent Kernel-Aware Unsupervised Skill Discovery

Unsupervised reinforcement learning (URL) aims to train general agents by learning transferable knowledge through interaction without external rewards, then adapting to downstream tasks with fewer interactions. Skill discovery learns distinguishable, controllable skills with broad coverage through intra-skill consistency and inter-skill diversity. Temporal distance, however, does not explicitly adapt local similarity scales to the empirical state distribution. We propose **I**solation **K**ernel-aware **S**kill **D**iscovery (IKSD), which constructs data-adaptive similarity and geometric scales in a latent space. Online IKSD constrains representation changes with IK dissimilarity; offline IKSD learns representation distances from cumulative IK-weighted transition costs. In DMC Walker and Cheetah, online IKSD achieves the highest final mean valid-posture path length on challenging terrain and competitive position coverage on flat ground. Experiments on fixed MetaWorld and BiGym datasets show that offline IKSD improves downstream performance and solves some tasks outside the data collection set.