Offline Goal-Conditioned Reinforcement Learning with Projective Quasimetric Planning
Abstract
Offline Goal-Conditioned Reinforcement Learning seeks to train agents to reach specified goals from previously collected trajectories. Scaling that promises to long-horizon tasks remains challenging, notably due to compounding value-estimation errors. Principled geometric offers a potential solution to address these issues. Following this insight, we introduce Projective Quasimetric Planning (ProQ), a compositional framework that learns an asymmetric distance and then repurposes it, firstly as a repulsive energy forcing a sparse set of keypoints to uniformly spread over the learned latent space, and secondly as a structured directional cost guiding towards proximal sub-goals. In particular, ProQ couples this geometry with a Lagrangian out-of-distribution detector to ensure the learned keypoints stay within reachable areas. By unifying metric learning, keypoint coverage, and goal-conditioned control, our approach produces meaningful sub-goals and robustly drives long-horizon goal-reaching on diverse a navigation benchmarks.
Cite
@article{arxiv.2506.18847,
title = {Offline Goal-Conditioned Reinforcement Learning with Projective Quasimetric Planning},
author = {Anthony Kobanda and Waris Radji and Mathieu Petitbois and Odalric-Ambrym Maillard and Rémy Portelas},
journal= {arXiv preprint arXiv:2506.18847},
year = {2026}
}