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

TL;DR

This paper presents a novel method for approximating viscosity solutions of complex Hamilton-Jacobi-Bellman equations in stochastic control, enhancing robustness and reducing violations through a min-max formulation.

Contribution

It introduces a viscosity enforcement approach as a min-max problem over an envelope-generated test family, improving solution accuracy in high-dimensional stochastic control.

Findings

Reduces empirical viscosity violations in numerical experiments.

Enhances robustness under perturbed dynamics.

Provides a new approximation method for viscosity solutions.

Abstract

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.