Policy iteration for nonconvex viscous Hamilton--Jacobi equations

We study the convergence rates of policy iteration (PI) for nonconvex viscous Hamilton–Jacobi equations using a discrete space-time scheme, where both space and time variables are discretized. We analyze the case with an uncontrolled diffusion term, which corresponds to a possibly degenerate viscous Hamilton–Jacobi equation. We first obtain an exponential convergent result of PI for the discrete space-time schemes. We then investigate the discretization error.