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.

翻译：我们通过离散时空格式研究策略迭代（PI）在非凸粘性 Hamilton-Jacobi 方程中的收敛速率，其中空间和时间变量均被离散化。我们分析了含不可控扩散项的情形，该情形对应可能退化的粘性 Hamilton-Jacobi 方程。首先获得了 PI 在离散时空格式中的指数收敛性结果，随后对离散化误差进行了分析。