Optimal Control From Inverse Scattering via Single-Sided Focusing

We describe an algorithm to solve Bellman optimization that replaces a sum over paths determining the optimal cost-to-go by an analytic method localized in state space. Our approach follows from the established relation between stochastic control problems in the class of linear Markov decision processes and quantum inverse scattering. We introduce a practical online computational method to solve for a potential function that informs optimal agent actions. This approach suggests that optimal control problems, including those with many degrees of freedom, can be solved with parallel computations.