Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability

Abstract:In goal-conditioned reinforcement learning (GCRL), quasimetric learning models goal-reaching costs as quasimetric distances, connecting local constraints to global value geometry. Its local constraints, however, should reflect the direction- dependent effects of control composition over a finite horizon together with environmental feasibility. We propose ReQRL, which constrains the critic's value gradients through finite-horizon reachability. Drawing on state-constrained optimal control, we decouple dynamical reachability from boundary geometry, estimating both from data. On OGBench, our method outperforms or rivals existing quasimetric approaches and other offline GCRL methods.

Machine Learning (cs.LG)

arXiv:2610.00778 [cs.LG]

(or arXiv:2610.00778v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.00778 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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