Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning

Tongzhou Wang, A. Torralba, Phillip Isola, Amy Zhang
2/12/2026

No official code found. Best implementation: quasimetric-learning/quasimetric-rl (62 stars, MIT, last commit 2025-05-19).

Abstract

In goal-reaching reinforcement learning (RL), the optimal value function has a particular geometry, called quasimetric structure. This paper introduces Quasimetric Reinforcement Learning (QRL), a new RL method that utilizes quasimetric models to learn optimal value functions. Distinct from prior approaches, the QRL objective is specifically designed for quasimetrics, and provides strong theoretical recovery guarantees. Empirically, we conduct thorough analyses on a discretized MountainCar environment, identifying properties of QRL and its advantages over alternatives. On offline and online goal-reaching benchmarks, QRL also demonstrates improved sample efficiency and performance, across both state-based and image-based observations.

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Code Implementations(1)

quasimetric-learning/quasimetric-rlCommunity100%
MIT

Open source code for paper "Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning" ICML 2023

6212Shell, PythonApr 28, 20231 years agoMIT

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Cite this paper

@article{wang2026optimal,
  title  = {Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning},
  author = {Tongzhou Wang and A. Torralba and Phillip Isola and Amy Zhang},
  year   = {2026},
  eprint = {2304.01203},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/pdf/2304.01203},
  journal = {ICML 2023 2023}
}

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