On the Power of Learning-Augmented Search Trees

Jingbang Chen, Xinyuan Cao, Alicia Stepin, Li Chen
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:7739-7762, 2025.

Abstract

We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each item $x$ is assigned a composite priority of $-\lfloor\log\log(1/w_x)\rfloor + U(0, 1)$ where $U(0, 1)$ is the uniform random variable. By choosing $w_x$ as the relative frequency of $x$, the resulting search trees achieve static optimality. This approach generalizes the recent learning-augmented BSTs [Lin-Luo-Woodruff ICML‘22], which only work for Zipfian distributions, by extending them to arbitrary input distributions. Furthermore, we demonstrate that our method can be generalized to a B-Tree data structure using the B-Treap approach [Golovin ICALP’09]. Our search trees are also capable of leveraging localities in the access sequence through online self-reorganization, thereby achieving the working-set property. Additionally, they are robust to prediction errors and support dynamic operations, such as insertions, deletions, and prediction updates. We complement our analysis with an empirical study, demonstrating that our method outperforms prior work and classic data structures.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-chen25e, title = {On the Power of Learning-Augmented Search Trees}, author = {Chen, Jingbang and Cao, Xinyuan and Stepin, Alicia and Chen, Li}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {7739--7762}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/chen25e/chen25e.pdf}, url = {https://proceedings.mlr.press/v267/chen25e.html}, abstract = {We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each item $x$ is assigned a composite priority of $-\lfloor\log\log(1/w_x)\rfloor + U(0, 1)$ where $U(0, 1)$ is the uniform random variable. By choosing $w_x$ as the relative frequency of $x$, the resulting search trees achieve static optimality. This approach generalizes the recent learning-augmented BSTs [Lin-Luo-Woodruff ICML‘22], which only work for Zipfian distributions, by extending them to arbitrary input distributions. Furthermore, we demonstrate that our method can be generalized to a B-Tree data structure using the B-Treap approach [Golovin ICALP’09]. Our search trees are also capable of leveraging localities in the access sequence through online self-reorganization, thereby achieving the working-set property. Additionally, they are robust to prediction errors and support dynamic operations, such as insertions, deletions, and prediction updates. We complement our analysis with an empirical study, demonstrating that our method outperforms prior work and classic data structures.} }
Endnote
%0 Conference Paper %T On the Power of Learning-Augmented Search Trees %A Jingbang Chen %A Xinyuan Cao %A Alicia Stepin %A Li Chen %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-chen25e %I PMLR %P 7739--7762 %U https://proceedings.mlr.press/v267/chen25e.html %V 267 %X We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each item $x$ is assigned a composite priority of $-\lfloor\log\log(1/w_x)\rfloor + U(0, 1)$ where $U(0, 1)$ is the uniform random variable. By choosing $w_x$ as the relative frequency of $x$, the resulting search trees achieve static optimality. This approach generalizes the recent learning-augmented BSTs [Lin-Luo-Woodruff ICML‘22], which only work for Zipfian distributions, by extending them to arbitrary input distributions. Furthermore, we demonstrate that our method can be generalized to a B-Tree data structure using the B-Treap approach [Golovin ICALP’09]. Our search trees are also capable of leveraging localities in the access sequence through online self-reorganization, thereby achieving the working-set property. Additionally, they are robust to prediction errors and support dynamic operations, such as insertions, deletions, and prediction updates. We complement our analysis with an empirical study, demonstrating that our method outperforms prior work and classic data structures.
APA
Chen, J., Cao, X., Stepin, A. & Chen, L.. (2025). On the Power of Learning-Augmented Search Trees. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:7739-7762 Available from https://proceedings.mlr.press/v267/chen25e.html.

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