# Meshfree Approximation for Stochastic Optimal Control Problems

arXiv: https://arxiv.org/abs/2104.09997 · HTML: https://mlsanity.com/paper/2104.09997/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [Federated Learning on Stochastic Neural Networks](https://mlsanity.com/paper/2506.08169/) (2025)

## Abstract (arXiv)

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.