Physics Informed Viscous Value Representations

• URL: http://arxiv.org/abs/2602.23280v1
• Date: Thu, 26 Feb 2026 17:53:46 GMT
• Title: Physics Informed Viscous Value Representations
• Authors: Hrishikesh Viswanath, Juanwu Lu, S. Talha Bukhari, Damon Conover, Ziran Wang, Aniket Bera,
• Abstract summary: We propose a physics-informed regularization of the viscosity solution of the Hamilton-Jacobi-Bellhikeman equation.<n>Our approach grounds the learning process in optimal control theory, explicitly regularizing and bounding updates during value iterations.<n> Experiments demonstrate that our method improves geometric consistency, making it broadly applicable to navigation and high-dimensional, complex manipulation tasks.
• Score: 18.60946729267083
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Offline goal-conditioned reinforcement learning (GCRL) learns goal-conditioned policies from static pre-collected datasets. However, accurate value estimation remains a challenge due to the limited coverage of the state-action space. Recent physics-informed approaches have sought to address this by imposing physical and geometric constraints on the value function through regularization defined over first-order partial differential equations (PDEs), such as the Eikonal equation. However, these formulations can often be ill-posed in complex, high-dimensional environments. In this work, we propose a physics-informed regularization derived from the viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation. By providing a physics-based inductive bias, our approach grounds the learning process in optimal control theory, explicitly regularizing and bounding updates during value iterations. Furthermore, we leverage the Feynman-Kac theorem to recast the PDE solution as an expectation, enabling a tractable Monte Carlo estimation of the objective that avoids numerical instability in higher-order gradients. Experiments demonstrate that our method improves geometric consistency, making it broadly applicable to navigation and high-dimensional, complex manipulation tasks. Open-source codes are available at https://github.com/HrishikeshVish/phys-fk-value-GCRL.

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