Quantizer Design for Finite Model Approximations, Model Learning, and Quantized Q-Learning for MDPs with Unbounded Spaces

Fuente: arXiv
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Autores principales: Bicer, Osman, Kara, Ali D., Yuksel, Serdar
Formato: Preprint
Publicado: 2025
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author Bicer, Osman
Kara, Ali D.
Yuksel, Serdar
author_facet Bicer, Osman
Kara, Ali D.
Yuksel, Serdar
contents In this paper, for Markov decision processes (MDPs) with unbounded state spaces we present refined upper bounds presented in [Kara et. al. JMLR'23] on finite model approximation errors via optimizing the quantizers used for finite model approximations. We also consider implications on quantizer design for quantized Q-learning and empirical model learning, and the performance of policies obtained via Q-learning where the quantized state is treated as the state itself. We highlight the distinctions between planning, where approximating MDPs can be independently designed, and learning (either via Q-learning or empirical model learning), where approximating MDPs are restricted to be defined by invariant measures of Markov chains under exploration policies, leading to significant subtleties on quantizer design performance, even though asymptotic near optimality can be established under both setups. In particular, under Lyapunov growth conditions, we obtain explicit upper bounds which decay to zero as the number of bins approaches infinity
format Preprint
id arxiv_https___arxiv_org_abs_2510_04355
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantizer Design for Finite Model Approximations, Model Learning, and Quantized Q-Learning for MDPs with Unbounded Spaces
Bicer, Osman
Kara, Ali D.
Yuksel, Serdar
Optimization and Control
Machine Learning
In this paper, for Markov decision processes (MDPs) with unbounded state spaces we present refined upper bounds presented in [Kara et. al. JMLR'23] on finite model approximation errors via optimizing the quantizers used for finite model approximations. We also consider implications on quantizer design for quantized Q-learning and empirical model learning, and the performance of policies obtained via Q-learning where the quantized state is treated as the state itself. We highlight the distinctions between planning, where approximating MDPs can be independently designed, and learning (either via Q-learning or empirical model learning), where approximating MDPs are restricted to be defined by invariant measures of Markov chains under exploration policies, leading to significant subtleties on quantizer design performance, even though asymptotic near optimality can be established under both setups. In particular, under Lyapunov growth conditions, we obtain explicit upper bounds which decay to zero as the number of bins approaches infinity
title Quantizer Design for Finite Model Approximations, Model Learning, and Quantized Q-Learning for MDPs with Unbounded Spaces
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2510.04355