用空间平滑约束替代传统微分约束,提升离线目标导向强化学习的值函数稳定性。
Mollified Value Learning
- 将距离约束转化为局部空间测度的期望,避免显式微分计算
- 在导航与机器人操作任务中显著提升目标达成成功率
- 适合高维复杂环境下的隐式值函数学习方法
离线目标导向强化学习(GCRL)从静态数据集中学习目标可达行为,但在状态-动作覆盖有限时准确估计价值仍具挑战。现有基于物理的方法通过哈密顿-雅可比-贝尔曼(HJB)最优性原理导出的点对点距离约束来解决,常以一阶偏微分方程(如Eikonal方程)实现。然而,在复杂高维环境中,强制局部一致性会因显式微分结构而变得不稳定。本文核心洞察是将距离类约束重释为局部空间测度上的期望。通过在该测度上聚合约束而非逐点评估,目标函数起到空间平滑作用,无需昂贵微分算子即可诱导距离类值几何结构。我们称此为“平滑值学习”(MVL)。在导航与高维机器人操控任务上的实验表明,结合隐式值表示学习方法,MVL能学习到结构化的值表示,显著提升目标达成性能。开源代码见:https://github.com/HrishikeshVish/MVL。
原文摘要 · Abstract (English)
Offline goal-conditioned reinforcement learning (GCRL) learns goal-reaching behaviors from static datasets, but accurate value estimation remains challenging under limited state-action coverage. Existing physics-informed approaches address this by imposing pointwise distance-like geometric constraints derived from Hamilton--Jacobi--Bellman (HJB) optimality principles, often through first-order partial differential equations such as the Eikonal equation. However, enforcing local consistency through explicit differential structure can become unstable in complex, high-dimensional environments. Our key insight is to instead reinterpret distance-like constraints as an expectation over a local spatial measure. By aggregating constraints over this measure rather than evaluating them pointwise, the objective acts as a spatial mollifier, inducing distance-like value geometry without requiring expensive differential operators. We refer to this as Mollified Value Learning (MVL). Experiments across navigation and high-dimensional robotic manipulation tasks show that MVL learns structured, value representations, improving goal-reaching performance, when used with implicit value representation learning methods. Open-source codes are available at https://github.com/HrishikeshVish/MVL.
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