Viscosity-Informed Generative Actor-Critic for High-Dimensional Stochastic Optimal Control
On the map: Deep reinforcement learning methods → RL theory and sample complexity
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.
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.
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7 of 27 references.
References · 7
- 2017Proximal Policy Optimization Algorithmscited by 15,215
- 2023Safety-Gymnasium: A Unified Safe Reinforcement Learning Benchmarkcited by 143
- 2021Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networkscited by 29
- 2022A Hamilton-Jacobi-based Proximal Operatorcited by 13
- 2023Bridging Physics-Informed Neural Networks with Reinforcement Learning: Hamilton-Jacobi-Bellman Proximal Policy Optimization (HJBPPO)cited by 7
- 2024Finite-difference least square methods for solving Hamilton-Jacobi equations using neural networkscited by 4
- 2023PINN-based viscosity solution of HJB equationcited by 1
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- 2025Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studies
- 2026An Actor-Critic Framework for Continuous-Time Jump-Diffusion Controls with Normalizing Flows
- 2024Solving Time-Continuous Stochastic Optimal Control Problems: Algorithm Design and Convergence Analysis of Actor-Critic Flow
- 2024On the stability of Lipschitz continuous control problems and its application to reinforcement learning
- 2024Compatible Gradient Approximations for Actor-Critic Algorithms
- 2025Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration
- 2025Convergence of Proximal Policy Gradient Method for Problems with Control Dependent Diffusion Coefficients
- 2026Learning to Solve Stochastic Controls with Unknown Drifts and Running Rewards: Theory, Algorithms and Convergence