High-probability sample complexities for policy evaluation with linear function approximation

Fuente: arXiv
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Autori principali: Li, Gen, Wu, Weichen, Chi, Yuejie, Ma, Cong, Rinaldo, Alessandro, Wei, Yuting
Natura: Preprint
Pubblicazione: 2023
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author Li, Gen
Wu, Weichen
Chi, Yuejie
Ma, Cong
Rinaldo, Alessandro
Wei, Yuting
author_facet Li, Gen
Wu, Weichen
Chi, Yuejie
Ma, Cong
Rinaldo, Alessandro
Wei, Yuting
contents This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation error of the best linear coefficients for two widely-used policy evaluation algorithms: the temporal difference (TD) learning algorithm and the two-timescale linear TD with gradient correction (TDC) algorithm. In both the on-policy setting, where observations are generated from the target policy, and the off-policy setting, where samples are drawn from a behavior policy potentially different from the target policy, we establish the first sample complexity bound with high-probability convergence guarantee that attains the optimal dependence on the tolerance level. We also exhihit an explicit dependence on problem-related quantities, and show in the on-policy setting that our upper bound matches the minimax lower bound on crucial problem parameters, including the choice of the feature maps and the problem dimension.
format Preprint
id arxiv_https___arxiv_org_abs_2305_19001
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle High-probability sample complexities for policy evaluation with linear function approximation
Li, Gen
Wu, Weichen
Chi, Yuejie
Ma, Cong
Rinaldo, Alessandro
Wei, Yuting
Machine Learning
Information Theory
Optimization and Control
Statistics Theory
This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation error of the best linear coefficients for two widely-used policy evaluation algorithms: the temporal difference (TD) learning algorithm and the two-timescale linear TD with gradient correction (TDC) algorithm. In both the on-policy setting, where observations are generated from the target policy, and the off-policy setting, where samples are drawn from a behavior policy potentially different from the target policy, we establish the first sample complexity bound with high-probability convergence guarantee that attains the optimal dependence on the tolerance level. We also exhihit an explicit dependence on problem-related quantities, and show in the on-policy setting that our upper bound matches the minimax lower bound on crucial problem parameters, including the choice of the feature maps and the problem dimension.
title High-probability sample complexities for policy evaluation with linear function approximation
topic Machine Learning
Information Theory
Optimization and Control
Statistics Theory
url https://arxiv.org/abs/2305.19001