Adaptive inference for functionals of M-estimands
Abstract
Reinforcement learning and contextual bandit algorithms have become increasingly common in sequential decision-making applications. When these methods are deployed in high-stakes domains, there is growing interest not only in learning effective policies, but also in conducting statistical inference for quantities learned under adaptive data collection. However, classical procedures applied naively in these settings can fail: even when estimators are unbiased, their variance becomes path-dependent and as a result may not be asymptotically normal. A growing literature has emerged to ameliorate this problem, but solutions tend to be problem specific and often rely on correct specification of a working model. In this work, we develop a unified framework for constructing asymptotically valid confidence intervals to cover smooth functionals of nonparametric M-estimands under adaptive sampling. Under Neyman orthogonality, we provide two novel methods for performing inference: (1) a self-normalized statistic based on the realized quadratic variation of the influence function and (2) a statistic using a plug-in estimate of the conditional variance based on reweighted influence function increments. Our results allow for flexible nonparametric estimation of nuisance parameters and remain valid under model misspecification. Our theory is supported by a simulation study for a dynamic pricing application which demonstrates that this method can produce asymptotically valid confidence intervals where standard methods fail.
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BibTeX
@misc{leiner2026adaptive,
title = {{Adaptive inference for functionals of M-estimands}},
author = {James Leiner and Aurélien Bibaut and Nathan Kallus and Aaditya Ramdas and Koulik Khamaru},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39274},
eprint = {2609.39274},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39274},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Adaptive inference for functionals of M-estimands
AU - James Leiner
AU - Aurélien Bibaut
AU - Nathan Kallus
AU - Aaditya Ramdas
AU - Koulik Khamaru
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39274
UR - https://arxiv.org/abs/2609.39274
AB - Reinforcement learning and contextual bandit algorithms have become increasingly common in sequential decision-making applications. When these methods are deployed in high-stakes domains, there is growing interest not only in learning effective policies, but also in conducting statistical inference for quantities learned under adaptive data collection. However, classical procedures applied naively in these settings can fail: even when estimators are unbiased, their variance becomes path-dependent and as a result may not be asymptotically normal. A growing literature has emerged to ameliorate this problem, but solutions tend to be problem specific and often rely on correct specification of a working model. In this work, we develop a unified framework for constructing asymptotically valid confidence intervals to cover smooth functionals of nonparametric M-estimands under adaptive sampling. Under Neyman orthogonality, we provide two novel methods for performing inference: (1) a self-normalized statistic based on the realized quadratic variation of the influence function and (2) a statistic using a plug-in estimate of the conditional variance based on reweighted influence function increments. Our results allow for flexible nonparametric estimation of nuisance parameters and remain valid under model misspecification. Our theory is supported by a simulation study for a dynamic pricing application which demonstrates that this method can produce asymptotically valid confidence intervals where standard methods fail.
ER -