Optimal Control From Inverse Scattering via Single-Sided Focusing

TL;DR

This paper introduces an analytic, localized method for solving Bellman optimal control problems by leveraging quantum inverse scattering, enabling efficient parallel computation for complex systems.

Contribution

It presents a novel algorithm connecting stochastic control with quantum inverse scattering, providing a practical online method for high-dimensional optimal control.

Findings

The method replaces path sums with an analytic localized approach.

It enables parallel computation for large-scale control problems.

The approach is applicable to systems with many degrees of freedom.

Abstract

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.