# Policy iteration for nonconvex viscous Hamilton--Jacobi equations

arXiv: https://arxiv.org/abs/2503.02159 · HTML: https://mlsanity.com/paper/2503.02159/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2025.

## Built on by (most cited first, 2 of 2)

- [Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration](https://mlsanity.com/paper/2507.15455/) (2025)
- [Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations](https://mlsanity.com/paper/2605.07116/) (2026)

## Abstract (arXiv)

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.