PINN-based viscosity solution of HJB equation

TL;DR

This paper introduces a PINN-based method for solving Hamilton-Jacobi-Bellman equations that guarantees viscosity solutions using convex neural networks, ensuring convergence to the true solution regardless of initial conditions.

Contribution

It presents a novel PINN approach employing convex neural networks to ensure viscosity solutions for HJB equations, addressing limitations of previous PINN methods.

Findings

Guarantees viscosity solutions with convex neural networks

Ensures neural network convergence to true HJB solutions

Addresses initial point sensitivity in solving HJB equations

Abstract

This paper proposed a novel PINN-based viscosity solution for HJB equations. Although there exists work using PINN to solve HJB, but none of them gives the solution in viscosity sense. This paper reveals the fact that using the convex neural network, one can guarantee the viscosity solution and thus the neural network can easily converge to the true solution of HJB despite of the starting point.