# 从有限时间可达性学习目标到达拟度量几何

> 原文链接：https://robotics.hellobike.com/papers/2026-09-30-2610-00778
> 频道：papers | 更新日期：2026-09-30 | 标签：arxiv, cs.RO
> 核心摘要：针对GCRL中拟度量约束需体现有限时域控制组合与环境可行性，ReQRL以有限时域可达性约束critic梯度，并在OGBench验证。

# 从有限时间可达性学习目标到达拟度量几何

::: v-pre
> 原文链接：[Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability](https://arxiv.org/abs/2610.00778)（arXiv 2610.00778 · 发布日期：2026-09-30）

**Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability**

针对GCRL中拟度量约束需体现有限时域控制组合与环境可行性，ReQRL以有限时域可达性约束critic梯度，并在OGBench验证。

## 核心要点

- GCRL中的拟度量学习将目标到达代价建模为距离，连接局部约束与全局价值几何。
- 局部约束需反映有限时域内控制组合的方向依赖效应以及环境可行性。
- ReQRL借鉴状态约束最优控制，解耦动力学可达性与边界几何并从数据估计。
- 在OGBench上，该方法优于或媲美现有拟度量方法和其他离线GCRL方法。

**验证范围与局限**：验证范围为OGBench；摘要未说明真机或其他场景。

## 英文摘要 (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.

作者：Daisuke Yamada, Travis Pence, Vikas Singh
:::

## 原始参考来源 (Sources)

- [arXiv 2610.00778：Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability](https://arxiv.org/abs/2610.00778)