Statistical Inference for Continuous Action Bandits
Abstract
Statistical inference under adaptively collected data is becoming increasingly popular across e-commerce and mobile health. Many methods exist for discrete action settings, ranging from weighting to debiasing approaches. Despite the ubiquity of continuous actions in experimentation from optimal pricing to precision dosing, to the best of our knowledge, methods that support statistical inference under continuous action, adaptively collected data remain underdeveloped. In this work, we extend kernel-smoothed doubly robust estimation from i.i.d. data to adaptively collected data with continuous actions. We study a family of adaptively weighted estimators, establish their mean squared error rates, asymptotic normality, and characterize an estimation lower bound as a function of regret. We conclude with recommendations for experimental design informing efficiency and regret, and support our theory with an extensive simulation study.
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BibTeX
@misc{kim2026statistical,
title = {{Statistical Inference for Continuous Action Bandits}},
author = {Raphael C Kim and Michele Santacatterina and Ramin Zabih and Rajarshi Mukherjee and Ivan Diaz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09801},
eprint = {2610.09801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09801},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Statistical Inference for Continuous Action Bandits
AU - Raphael C Kim
AU - Michele Santacatterina
AU - Ramin Zabih
AU - Rajarshi Mukherjee
AU - Ivan Diaz
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09801
UR - https://arxiv.org/abs/2610.09801
AB - Statistical inference under adaptively collected data is becoming increasingly popular across e-commerce and mobile health. Many methods exist for discrete action settings, ranging from weighting to debiasing approaches. Despite the ubiquity of continuous actions in experimentation from optimal pricing to precision dosing, to the best of our knowledge, methods that support statistical inference under continuous action, adaptively collected data remain underdeveloped. In this work, we extend kernel-smoothed doubly robust estimation from i.i.d. data to adaptively collected data with continuous actions. We study a family of adaptively weighted estimators, establish their mean squared error rates, asymptotic normality, and characterize an estimation lower bound as a function of regret. We conclude with recommendations for experimental design informing efficiency and regret, and support our theory with an extensive simulation study.
ER -