# Rates of Convergence in Certain Native Spaces of Approximations used in Reinforcement Learning

arXiv: https://arxiv.org/abs/2309.07383 · HTML: https://mlsanity.com/paper/2309.07383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 25 references that are in the map.
- First posted on arXiv 14 Sep 2023.

## Builds on (most cited first, 2 of 2)

- [Robust feedback control of nonlinear PDEs by numerical approximation of high-dimensional Hamilton-Jacobi-Isaacs equations](https://mlsanity.com/paper/1905.06276/) (2019)
- [Rates of convergence for the policy iteration method for Mean Field Games systems](https://mlsanity.com/paper/2108.00755/) (2021)

## Abstract (arXiv)

This paper studies convergence rates for some value function approximations that arise in a collection of reproducing kernel Hilbert spaces (RKHS) H(Omega). By casting an optimal control problem in a specific class of native spaces, strong rates of convergence are derived for the operator equation that enables offline approximations that appear in policy iteration. Explicit upper bounds on error in value function and controller approximations are derived in terms of power function PH,N for the space of finite dimensional approximants HN in the native space H(Omega). These bounds are geometric in nature and refine some well-known, now classical results concerning convergence of approximations of value functions.