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arXiv · 2506.18847

Offline Goal-Conditioned Reinforcement Learning with Projective Quasimetric Planning

Anthony Kobanda·Waris Radji·Mathieu Petitbois·Odalric-Ambrym Maillard·Rémy Portelas
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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.

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Anthony Kobanda, Waris Radji, Mathieu Petitbois, Odalric-Ambrym Maillard, Rémy Portelas. 2025-06-23. Offline Goal-Conditioned Reinforcement Learning with Projective Quasimetric Planning. https://arxiv.org/abs/2506.18847

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