Adaptive Quasimetric Mapping : Principled Topological Abstraction for Robust Offline Goal-Conditioned Navigation

Goal-Conditioned Reinforcement Learning aims to design agents that can reach specified goals, notably from previously collected trajectories in the offline setting. In this context, graph-based approaches have been proposed to mitigate compounding value-estimation errors in long-horizon navigation tasks. However, existing approaches typically rely on dense keypoint coverage of the dataset support, resulting in computationally expensive planning. Moreover, they lack explicit mechanisms to adapt to topological changes (e.g., new obstacles), hindering deployment in live applications such as video game environments. To address these two shortcomings, we introduce Adaptive Quasimetric Mapping (AQM), an offline framework leveraging a “time-to-reach” quasimetric learned from the available data. Crucially, it builds a sparse cover of the dataset support, as a greedy approximation to a dominating set problem. At test-time, the resulting graph is carefully pruned by comparing the observed edge traversal time against a time-to-reach budget derived from the quasimetric, thus enabling zero-shot replanning. Empirically, we evaluate AQM on navigation tasks ranging from a classical to a video-game-like benchmark evaluating adaptation across tasks. We show that AQM achieves competitive performance while requiring up to 100× fewer keypoints than prior approaches, hence demonstrating the relevance of topological abstraction for goal-conditioned navigation.