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.
Convergence of approximation schemes for fully nonlinear second order equations.Asymptotic analysis, 4(3):271–283, 1991
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A travel-cost value function defined via a proposed running cost is the unique bounded viscosity solution to a time-dependent HJB PDE whose negative sublevel set is the strict backward-reachable tube, and small-step RL value iteration converges to the forward discounted HJB solution.
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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.
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Unifying Hamilton-Jacobi Reachability and Reinforcement Learning
A travel-cost value function defined via a proposed running cost is the unique bounded viscosity solution to a time-dependent HJB PDE whose negative sublevel set is the strict backward-reachable tube, and small-step RL value iteration converges to the forward discounted HJB solution.