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Viscosity-Informed Generative Actor-Critic for High-Dimensional Stochastic Optimal Control
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.
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BibTeX
@misc{golpashin2026viscosityinformed,
title = {{Viscosity-Informed Generative Actor-Critic for High-Dimensional Stochastic Optimal Control}},
author = {Alen E. Golpashin and Gokul Puthumanaillam and Melkior Ornik and Bruce A. Conway},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.15668},
eprint = {2605.15668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15668},
}
RIS
TY - UNPB
TI - Viscosity-Informed Generative Actor-Critic for High-Dimensional Stochastic Optimal Control
AU - Alen E. Golpashin
AU - Gokul Puthumanaillam
AU - Melkior Ornik
AU - Bruce A. Conway
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2605.15668
UR - https://arxiv.org/abs/2605.15668
AB - 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.
ER -