# Viscosity-Informed Generative Actor-Critic for High-Dimensional Stochastic Optimal Control

arXiv: https://arxiv.org/abs/2605.15668 · HTML: https://mlsanity.com/paper/2605.15668/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 15 May 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 7 of 7)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Safety-Gymnasium: A Unified Safe Reinforcement Learning Benchmark](https://mlsanity.com/paper/2310.12567/) (2023)
- [Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks](https://mlsanity.com/paper/2102.11379/) (2021)
- [A Hamilton-Jacobi-based Proximal Operator](https://mlsanity.com/paper/2211.12997/) (2022)
- [Bridging Physics-Informed Neural Networks with Reinforcement Learning: Hamilton-Jacobi-Bellman Proximal Policy Optimization (HJBPPO)](https://mlsanity.com/paper/2302.00237/) (2023)
- [Finite-difference least square methods for solving Hamilton-Jacobi equations using neural networks](https://mlsanity.com/paper/2406.10758/) (2024)
- [PINN-based viscosity solution of HJB equation](https://mlsanity.com/paper/2309.09953/) (2023)

## Abstract (arXiv)

We introduce a method for approximating viscosity solutions of stationary degenerate elliptic Hamilton--Jacobi--Bellman equations on bounded domains arising in stochastic exit-time control. Viscosity enforcement is formulated as a min--max problem over an envelope-generated test family parameterized by symmetric positive definite matrices. Under structural and asymptotic assumptions, any uniform limit point of the value function approximations satisfies the viscosity inequalities on the sampled test family. Numerical experiments show that the proposed method reduces empirical viscosity violations and improves robustness under perturbed dynamics.