Near-Optimal Confidence Sequences for Bounded Random Variables

Arun K Kuchibhotla, Qinqing Zheng
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:5827-5837, 2021.

Abstract

Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence intervals that are valid uniformly over the growing-into-infinity sample sizes. To address this question, we provide a near-optimal confidence sequence for bounded random variables by utilizing Bentkus’ concentration results. We show that it improves on the existing approaches that use the Cram{é}r-Chernoff technique such as the Hoeffding, Bernstein, and Bennett inequalities. The resulting confidence sequence is confirmed to be favorable in synthetic coverage problems, adaptive stopping algorithms, and multi-armed bandit problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-kuchibhotla21a, title = {Near-Optimal Confidence Sequences for Bounded Random Variables}, author = {Kuchibhotla, Arun K and Zheng, Qinqing}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {5827--5837}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/kuchibhotla21a/kuchibhotla21a.pdf}, url = {https://proceedings.mlr.press/v139/kuchibhotla21a.html}, abstract = {Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence intervals that are valid uniformly over the growing-into-infinity sample sizes. To address this question, we provide a near-optimal confidence sequence for bounded random variables by utilizing Bentkus’ concentration results. We show that it improves on the existing approaches that use the Cram{é}r-Chernoff technique such as the Hoeffding, Bernstein, and Bennett inequalities. The resulting confidence sequence is confirmed to be favorable in synthetic coverage problems, adaptive stopping algorithms, and multi-armed bandit problems.} }
Endnote
%0 Conference Paper %T Near-Optimal Confidence Sequences for Bounded Random Variables %A Arun K Kuchibhotla %A Qinqing Zheng %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-kuchibhotla21a %I PMLR %P 5827--5837 %U https://proceedings.mlr.press/v139/kuchibhotla21a.html %V 139 %X Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence intervals that are valid uniformly over the growing-into-infinity sample sizes. To address this question, we provide a near-optimal confidence sequence for bounded random variables by utilizing Bentkus’ concentration results. We show that it improves on the existing approaches that use the Cram{é}r-Chernoff technique such as the Hoeffding, Bernstein, and Bennett inequalities. The resulting confidence sequence is confirmed to be favorable in synthetic coverage problems, adaptive stopping algorithms, and multi-armed bandit problems.
APA
Kuchibhotla, A.K. & Zheng, Q.. (2021). Near-Optimal Confidence Sequences for Bounded Random Variables. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:5827-5837 Available from https://proceedings.mlr.press/v139/kuchibhotla21a.html.

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