@inproceedings{
nguyen2024active,
title={Active Set Ordering},
author={Quoc Phong Nguyen and Sunil Gupta and Svetha Venkatesh and Bryan Kian Hsiang Low and Patrick Jaillet},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=GkJbXpd3wM}
}
In this paper, we formalize the active set ordering problem, which involves actively discovering a set of inputs based on their orderings determined by expensive evaluations of a blackbox function. We then propose the mean prediction (MP) algorithm and theoretically analyze it  in terms of the regret of predicted pairwise orderings between inputs. Notably, as a special case of this framework, we can cast Bayesian optimization as an active set ordering problem by recognizing that maximizers can be identified solely by comparison rather than by precisely estimating the function evaluations. As a result, we are able to construct the popular Gaussian process upper confidence bound (GP-UCB) algorithm through the lens of ordering with several nuanced insights. We empirically validate the performance of our proposed solution using various synthetic functions and real-world datasets.
Active Set Ordering
Quoc Phong Nguyen Sunil Gupta Svetha Venkatesh Bryan Kian Hsiang Low Patrick Jaillet