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.
User’s guide to viscosity solutions of second order partial differential equations.Bulletin of the American mathematical society, 27(1):1–67, 1992
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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.