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Main Authors: Chen, Xingguo, Wu, Chaohui, Ye, Jinguo, Li, Chao, Yang, Shangdong, Yang, Guang, Liang, Tianyu, Wang, Wenhao
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2605.04100
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author Chen, Xingguo
Wu, Chaohui
Ye, Jinguo
Li, Chao
Yang, Shangdong
Yang, Guang
Liang, Tianyu
Wang, Wenhao
author_facet Chen, Xingguo
Wu, Chaohui
Ye, Jinguo
Li, Chao
Yang, Shangdong
Yang, Guang
Liang, Tianyu
Wang, Wenhao
contents Off-policy temporal-difference (TD) learning with function approximation faces a structural tradeoff among stability, projection geometry, and variance control. Emphatic TD (ETD) improves the off-policy projection geometry through follow-on emphasis, but the follow-on trace can have high variance. We revisit this tradeoff through Bellman-error centering. Although centering naturally removes a common drift term from TD errors, we show that a naive centered emphatic extension introduces an auxiliary coupling that can destroy the positive-definiteness of the ETD key matrix. We propose \emph{Regularized Emphatic Temporal-Difference Learning} (RETD), which preserves the follow-on trace and regularizes only the auxiliary centering recursion, corresponding to lifting the lower-right block of the coupled key matrix from \(1\) to \(1+c\). We derive the RETD core matrix, prove convergence under a conservative sufficient regularization condition, and evaluate the method on diagnostic linear off-policy prediction tasks. The experiments show that RETD avoids the instability of naive centered emphatic learning, preserves favorable emphatic geometry, and exhibits a robust intermediate regime for the regularization parameter \(c\) across the diagnostics.
format Preprint
id arxiv_https___arxiv_org_abs_2605_04100
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Regularized Centered Emphatic Temporal Difference Learning
Chen, Xingguo
Wu, Chaohui
Ye, Jinguo
Li, Chao
Yang, Shangdong
Yang, Guang
Liang, Tianyu
Wang, Wenhao
Artificial Intelligence
Off-policy temporal-difference (TD) learning with function approximation faces a structural tradeoff among stability, projection geometry, and variance control. Emphatic TD (ETD) improves the off-policy projection geometry through follow-on emphasis, but the follow-on trace can have high variance. We revisit this tradeoff through Bellman-error centering. Although centering naturally removes a common drift term from TD errors, we show that a naive centered emphatic extension introduces an auxiliary coupling that can destroy the positive-definiteness of the ETD key matrix. We propose \emph{Regularized Emphatic Temporal-Difference Learning} (RETD), which preserves the follow-on trace and regularizes only the auxiliary centering recursion, corresponding to lifting the lower-right block of the coupled key matrix from \(1\) to \(1+c\). We derive the RETD core matrix, prove convergence under a conservative sufficient regularization condition, and evaluate the method on diagnostic linear off-policy prediction tasks. The experiments show that RETD avoids the instability of naive centered emphatic learning, preserves favorable emphatic geometry, and exhibits a robust intermediate regime for the regularization parameter \(c\) across the diagnostics.
title Regularized Centered Emphatic Temporal Difference Learning
topic Artificial Intelligence
url https://arxiv.org/abs/2605.04100