Online Individualized Treatment Selection under Partial Feedback: False Discovery Control and Minimax Optimality
Abstract
We study online individualized treatment selection when only the outcome under the assigned treatment is observed. Our objective is to preferentially treat individuals whose potential outcomes under treatment exceed a covariate-specific control reference, while limiting false discoveries among treated individuals. We propose Partial-Feedback Adaptive Individualized Treatment Selection (PAITS), which initializes learning from historical data and combines sequential estimation of local null risks, randomized exploration, and feedback-driven updates of the treatment selection threshold. Under regularity conditions, we establish asymptotic false discovery rate control and sublinear gap-weighted assignment regret relative to a population oracle. We further establish a minimax lower bound on assignment regret under prescribed uniform nuisance-estimation requirements and give conditions under which PAITS attains the corresponding constrained minimax rate up to logarithmic factors. These results quantify the tradeoff between accurate treatment assignment and nuisance learning under partial feedback. Simulation studies and a real-data analysis using the Jester recommendation dataset illustrate the finite-sample performance of PAITS.
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BibTeX
@misc{gu2026online,
title = {{Online Individualized Treatment Selection under Partial Feedback: False Discovery Control and Minimax Optimality}},
author = {Runzhe Gu and Zinan Zhao and Wenguang Sun and Xintao Xia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16464},
eprint = {2610.16464},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16464},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Online Individualized Treatment Selection under Partial Feedback: False Discovery Control and Minimax Optimality
AU - Runzhe Gu
AU - Zinan Zhao
AU - Wenguang Sun
AU - Xintao Xia
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16464
UR - https://arxiv.org/abs/2610.16464
AB - We study online individualized treatment selection when only the outcome under the assigned treatment is observed. Our objective is to preferentially treat individuals whose potential outcomes under treatment exceed a covariate-specific control reference, while limiting false discoveries among treated individuals. We propose Partial-Feedback Adaptive Individualized Treatment Selection (PAITS), which initializes learning from historical data and combines sequential estimation of local null risks, randomized exploration, and feedback-driven updates of the treatment selection threshold. Under regularity conditions, we establish asymptotic false discovery rate control and sublinear gap-weighted assignment regret relative to a population oracle. We further establish a minimax lower bound on assignment regret under prescribed uniform nuisance-estimation requirements and give conditions under which PAITS attains the corresponding constrained minimax rate up to logarithmic factors. These results quantify the tradeoff between accurate treatment assignment and nuisance learning under partial feedback. Simulation studies and a real-data analysis using the Jester recommendation dataset illustrate the finite-sample performance of PAITS.
ER -