Huber-robust confidence sequences

Hongjian Wang, Aaditya Ramdas
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:9662-9679, 2023.

Abstract

Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the p-th central moment (p $>$ 1), but allowing for (at most) $\varepsilon$ fraction of arbitrary distribution corruption, as in Huber’s contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisingly, the constant margin between our sequential result and the lower bound is smaller than even fixed-time robust confidence intervals based on the trimmed mean, for example. Since confidence sequences are a common tool used within A/B/n testing and bandits, these results open the door to sequential experimentation that is robust to outliers and adversarial corruptions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-wang23p, title = {Huber-robust confidence sequences}, author = {Wang, Hongjian and Ramdas, Aaditya}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {9662--9679}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/wang23p/wang23p.pdf}, url = {https://proceedings.mlr.press/v206/wang23p.html}, abstract = {Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the p-th central moment (p $>$ 1), but allowing for (at most) $\varepsilon$ fraction of arbitrary distribution corruption, as in Huber’s contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisingly, the constant margin between our sequential result and the lower bound is smaller than even fixed-time robust confidence intervals based on the trimmed mean, for example. Since confidence sequences are a common tool used within A/B/n testing and bandits, these results open the door to sequential experimentation that is robust to outliers and adversarial corruptions.} }
Endnote
%0 Conference Paper %T Huber-robust confidence sequences %A Hongjian Wang %A Aaditya Ramdas %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-wang23p %I PMLR %P 9662--9679 %U https://proceedings.mlr.press/v206/wang23p.html %V 206 %X Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the p-th central moment (p $>$ 1), but allowing for (at most) $\varepsilon$ fraction of arbitrary distribution corruption, as in Huber’s contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisingly, the constant margin between our sequential result and the lower bound is smaller than even fixed-time robust confidence intervals based on the trimmed mean, for example. Since confidence sequences are a common tool used within A/B/n testing and bandits, these results open the door to sequential experimentation that is robust to outliers and adversarial corruptions.
APA
Wang, H. & Ramdas, A.. (2023). Huber-robust confidence sequences. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:9662-9679 Available from https://proceedings.mlr.press/v206/wang23p.html.

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