Learning with Comparison Feedback: Online Estimation of Sample Statistics
Abstract
We study an online version of the noisy binary search problem where feedback is generated by a non-stochastic adversary rather than perturbed by random noise. We reframe this as maintaining an accurate estimate for the median of an adversarial sequence of integers, $x_1, x_2, …$, in a model where each number $x_t$ can only be accessed through a single threshold query of the form ${1(x_t \leq q_t)}$. In this online comparison feedback model, we explore estimation of general sample statistics, providing robust algorithms for median, CDF, and mean estimation with nearly matching lower bounds. We conclude with several high-dimensional generalizations.
Cite
Text
Meister and Nietert. "Learning with Comparison Feedback: Online Estimation of Sample Statistics." Proceedings of the 32nd International Conference on Algorithmic Learning Theory, 2021.Markdown
[Meister and Nietert. "Learning with Comparison Feedback: Online Estimation of Sample Statistics." Proceedings of the 32nd International Conference on Algorithmic Learning Theory, 2021.](https://mlanthology.org/alt/2021/meister2021alt-learning/)BibTeX
@inproceedings{meister2021alt-learning,
title = {{Learning with Comparison Feedback: Online Estimation of Sample Statistics}},
author = {Meister, Michela and Nietert, Sloan},
booktitle = {Proceedings of the 32nd International Conference on Algorithmic Learning Theory},
year = {2021},
pages = {983-1001},
volume = {132},
url = {https://mlanthology.org/alt/2021/meister2021alt-learning/}
}