ACTOR-CRITIC METHOD FOR HIGH DIMENSIONAL STATIC HAMILTON-JACOBI-BELLMAN PARTIAL DIFFERENTIAL EQUATIONS BASED ON NEURAL NETWORKS

Journal Article (Journal Article)

We propose a novel numerical method for high dimensional Hamilton-Jacobi-Bellman (HJB) type elliptic partial differential equations (PDEs). The HJB PDEs, reformulated as optimal control problems, are tackled by the actor-critic framework inspired by reinforcement learning, based on neural network parametrization of the value and control functions. Within the actor-critic framework, we employ a policy gradient approach to improve the control, while for the value function, we derive a variance reduced least-squares temporal difference method using stochastic calculus. To numerically discretize the stochastic control problem, we employ an adaptive step size scheme to improve the accuracy near the domain boundary. Numerical examples up to 20 spatial dimensions including the linear quadratic regulators, the stochastic Van der Pol oscillators, the diffusive Eikonal equations, and fully nonlinear elliptic PDEs derived from a regulator problem are presented to validate the effectiveness of our proposed method.

Full Text

Duke Authors

Cited Authors

  • Zhou, M; Han, J; Lu, J

Published Date

  • January 1, 2021

Published In

Volume / Issue

  • 43 / 6

Start / End Page

  • A4043 - A4066

Electronic International Standard Serial Number (EISSN)

  • 1095-7197

International Standard Serial Number (ISSN)

  • 1064-8275

Digital Object Identifier (DOI)

  • 10.1137/21M1402303

Citation Source

  • Scopus