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Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability

arXiv 2610.00778 ↗First posted 30 Sep 2026cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 26 of its 49 references that are in the map. First posted on arXiv 30 Sep 2026.

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References · 26

  1. 2015Continuous control with deep reinforcement learningcited by 3,279
  2. 2021Offline Reinforcement Learning with Implicit Q-Learningcited by 1,245
  3. 2019Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learningcited by 750
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  10. 2023Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learningcited by 116
  11. 2018Temporal Difference Models: Model-Free Deep RL for Model-Based Controlcited by 89
  12. 2022Rethinking Goal-conditioned Supervised Learning and Its Connection to Offline RLcited by 89
14 more
  1. 2024Foundation Policies with Hilbert Representationscited by 89
  2. 2019Dynamical Distance Learning for Semi-Supervised and Unsupervised Skill Discoverycited by 65
  3. 2022How Far I'll Go: Offline Goal-Conditioned Reinforcement Learning via f-Advantage Regressioncited by 65
  4. 2024Learning Temporal Distances: Contrastive Successor Features Can Provide a Metric Structure for Decision-Makingcited by 53
  5. 2022Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddingscited by 22
  6. 2025Option-aware Temporally Abstracted Value for Offline Goal-Conditioned Reinforcement Learningcited by 22
  7. 2020Plan2Vec: Unsupervised Representation Learning by Latent Planscited by 21
  8. 2025Offline Goal-conditioned Reinforcement Learning with Quasimetric Representationscited by 20
  9. 2025Physics-informed Value Learner for Offline Goal-Conditioned Reinforcement Learningcited by 15
  10. 2025Graph-Assisted Stitching for Offline Hierarchical Reinforcement Learningcited by 12
  11. 2025Flattening Hierarchies with Policy Bootstrappingcited by 8
  12. 2023Data-driven Reachability using Christoffel Functions and Conformal Predictioncited by 6
  13. 2025Goal Reaching with Eikonal-Constrained Hierarchical Quasimetric Reinforcement Learningcited by 6
  14. 2016Inverse Problems for Matrix Exponential in System Identification: System Aliasingcited by 3

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