A monotone semi-discrete policy iteration scheme with O(h) artificial viscosity for stationary discounted HJB equations converges geometrically for fixed h and achieves O(sqrt(h)) error to the viscosity solution.
Exponential convergence and stability of howard’s policy improvement algorithm for controlled diffusions.SIAM Journal on Control and Optimization, 58(3):1314–1340, 2020
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Policy Iteration for Stationary Discounted Hamilton--Jacobi--Bellman Equations: A Viscosity Approach
A monotone semi-discrete policy iteration scheme with O(h) artificial viscosity for stationary discounted HJB equations converges geometrically for fixed h and achieves O(sqrt(h)) error to the viscosity solution.