Feedback-Aware Tuning of Recursive Q-Learning
Abstract
Model choice in backward Q-learning is recursive because a later-stage choice changes the response supplied to an earlier regression and can alter its model-comparison statistic. Separate stagewise criteria do not directly assess the target-stage prediction risk of a completed Q-learning fit. We address this mismatch by treating the entire backward-fitting rule as the unit of comparison and propose feedback-aware soft tuning for sequential multiple assignment randomised trials. Each backward fit uses its own generated responses and is assessed at a common prediction target. The risk criterion retains downstream effects on upstream comparisons, while a separate correction accounts for estimating the final exponential weights from the same observations. For a fixed finite library of smooth recursive maps, we establish an exact risk identity under a Gaussian shift model and an oracle inequality with an explicit adaptation remainder. Under coordinate-representation and moment conditions, these guarantees transfer to prediction risk at any prespecified stage, with the number of stages fixed as sample size increases. A two-stage construction supplies an explicit observable implementation. Numerical studies examine risk estimation and finite-sample performance, and a simulated attention-deficit/hyperactivity-disorder trial illustrates the relation between comparison feedback and treatment recommendations.
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BibTeX
@misc{kojima2026feedbackaware,
title = {{Feedback-Aware Tuning of Recursive Q-Learning}},
author = {Masahiro Kojima},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12716},
eprint = {2609.12716},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12716},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Feedback-Aware Tuning of Recursive Q-Learning
AU - Masahiro Kojima
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12716
UR - https://arxiv.org/abs/2609.12716
AB - Model choice in backward Q-learning is recursive because a later-stage choice changes the response supplied to an earlier regression and can alter its model-comparison statistic. Separate stagewise criteria do not directly assess the target-stage prediction risk of a completed Q-learning fit. We address this mismatch by treating the entire backward-fitting rule as the unit of comparison and propose feedback-aware soft tuning for sequential multiple assignment randomised trials. Each backward fit uses its own generated responses and is assessed at a common prediction target. The risk criterion retains downstream effects on upstream comparisons, while a separate correction accounts for estimating the final exponential weights from the same observations. For a fixed finite library of smooth recursive maps, we establish an exact risk identity under a Gaussian shift model and an oracle inequality with an explicit adaptation remainder. Under coordinate-representation and moment conditions, these guarantees transfer to prediction risk at any prespecified stage, with the number of stages fixed as sample size increases. A two-stage construction supplies an explicit observable implementation. Numerical studies examine risk estimation and finite-sample performance, and a simulated attention-deficit/hyperactivity-disorder trial illustrates the relation between comparison feedback and treatment recommendations.
ER -