Meshfree Approximation for Stochastic Optimal Control Problems

TL;DR

This paper develops a meshfree approximation framework using gradient projection for high-dimensional stochastic control problems, validated through numerical experiments and convergence analysis.

Contribution

It extends the gradient projection method to higher dimensions using meshfree techniques like moving least squares and radial basis functions.

Findings

Convergence of the meshfree approximation is rigorously proven.

Numerical experiments validate the effectiveness of the approach.

The method efficiently solves high-dimensional stochastic control problems.

Abstract

In this work, we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation approach to implement spatial dimension approximation. Our main contribution is to extend the existing gradient projection method to moderate high-dimensional space. The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework, and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach. We also present several numerical experiments to validate the theoretical results of our approach and demonstrate the performance meshfree approximation in solving stochastic optimal control problems.