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arXiv · 2610.00778

Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability

Daisuke Yamada·Travis Pence·Vikas Singh
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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.

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Daisuke Yamada, Travis Pence, Vikas Singh. 2026-09-30. Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability. https://arxiv.org/abs/2610.00778

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