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

Autor:	Bouland, Ali, Niu, Shengyuan, Paruchuri, Sai Tej, Kurdila, Andrew, Burns, John, Schuster, Eugenio
Rok vydání:	2023
Předmět:	Electrical Engineering and Systems Science - Systems and Control Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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 $\mathcal{P}_{H,N}$ for the space of finite dimensional approximants $H_N$ 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. Comment: 8 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.07383 Zobrazit plný text záznamu View this record from Arxiv