Secretary Problem with Predictions and Ordering

Kang Yiming
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:352-360, 2026.

Abstract

The classic secretary problem, a cornerstone of optimal stopping theory, assumes a random, immutable arrival order of candidates. While recent work has integrated machine-learned predictions to improve selection, the power to set the arrival order based on these predictions remains largely untapped. This paper introduces a novel framework for the secretary problem that leverages predictions for both valuation and strategic scheduling. We propose an algorithm that strategically controls the arrival time of the top-predicted candidate and dynamically adapts its hiring policy based on observed prediction accuracy. Our analysis shows that this approach achieves a worst-case competitive ratio of 0.229, surpassing the 0.215 bound of state-of-the-art algorithms that do not control ordering, bringing it closer to the upper bound of $1/e \approx 0.368$ while maintaining consistency guarantees. Furthermore, we demonstrate that our ordering framework can be adapted to improve fairness guarantees, doubling the success probability in a known fair algorithm from 1/16 to 1/8. Our results highlight that controlling the sequence is a powerful tool for building more robust and fair learning-augmented online algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-yiming26a, title = { Secretary Problem with Predictions and Ordering }, author = {Yiming, Kang}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {352--360}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/yiming26a/yiming26a.pdf}, url = {https://proceedings.mlr.press/v300/yiming26a.html}, abstract = { The classic secretary problem, a cornerstone of optimal stopping theory, assumes a random, immutable arrival order of candidates. While recent work has integrated machine-learned predictions to improve selection, the power to set the arrival order based on these predictions remains largely untapped. This paper introduces a novel framework for the secretary problem that leverages predictions for both valuation and strategic scheduling. We propose an algorithm that strategically controls the arrival time of the top-predicted candidate and dynamically adapts its hiring policy based on observed prediction accuracy. Our analysis shows that this approach achieves a worst-case competitive ratio of 0.229, surpassing the 0.215 bound of state-of-the-art algorithms that do not control ordering, bringing it closer to the upper bound of $1/e \approx 0.368$ while maintaining consistency guarantees. Furthermore, we demonstrate that our ordering framework can be adapted to improve fairness guarantees, doubling the success probability in a known fair algorithm from 1/16 to 1/8. Our results highlight that controlling the sequence is a powerful tool for building more robust and fair learning-augmented online algorithms. } }
Endnote
%0 Conference Paper %T Secretary Problem with Predictions and Ordering %A Kang Yiming %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-yiming26a %I PMLR %P 352--360 %U https://proceedings.mlr.press/v300/yiming26a.html %V 300 %X The classic secretary problem, a cornerstone of optimal stopping theory, assumes a random, immutable arrival order of candidates. While recent work has integrated machine-learned predictions to improve selection, the power to set the arrival order based on these predictions remains largely untapped. This paper introduces a novel framework for the secretary problem that leverages predictions for both valuation and strategic scheduling. We propose an algorithm that strategically controls the arrival time of the top-predicted candidate and dynamically adapts its hiring policy based on observed prediction accuracy. Our analysis shows that this approach achieves a worst-case competitive ratio of 0.229, surpassing the 0.215 bound of state-of-the-art algorithms that do not control ordering, bringing it closer to the upper bound of $1/e \approx 0.368$ while maintaining consistency guarantees. Furthermore, we demonstrate that our ordering framework can be adapted to improve fairness guarantees, doubling the success probability in a known fair algorithm from 1/16 to 1/8. Our results highlight that controlling the sequence is a powerful tool for building more robust and fair learning-augmented online algorithms.
APA
Yiming, K.. (2026). Secretary Problem with Predictions and Ordering . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:352-360 Available from https://proceedings.mlr.press/v300/yiming26a.html.

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