Dynamic programming using radial basis functions

TL;DR

This paper introduces a new discretization method for dynamic programming using radial basis functions and Shepard's approximation, with proven convergence and demonstrated through numerical experiments.

Contribution

It presents a novel discretization approach for dynamic programming leveraging radial basis functions and Shepard's method, with theoretical convergence guarantees.

Findings

Convergence of the approximate value function to the true solution.

Effective numerical experiments demonstrating the method.

Potential for improved discretization in dynamic programming.

Abstract

We propose a discretization of the optimality principle in dynamic programming based on radial basis functions and Shepard's moving least squares approximation method. We prove convergence of the approximate optimal value function to the true one and present several numerical experiments.