Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization

Donney Fan, Geoff Pleiss
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3736-3744, 2026.

Abstract

In Bayesian optimization, Thompson sampling selects the evaluation point by sampling from the posterior distribution over the objective function maximizer. Because this sampling problem is intractable for Gaussian process (GP) surrogates, the posterior distribution is typically restricted to fixed discretizations (i.e., candidate points) that become exponentially sparse as dimensionality increases. While previous works aim to increase candidate point density through scalable GP approximations, our orthogonal approach increases density by adaptively reducing the search space during sampling. Specifically, we introduce Adaptive Candidate Thompson Sampling (ACTS), which generates candidate points in subspaces guided by the gradient of a surrogate model sample. ACTS is a simple drop-in replacement for existing TS methods—including those that use trust regions or other local approximations—producing better samples of maxima and improved optimization across synthetic and real-world benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-fan26c, title = { Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization }, author = {Fan, Donney and Pleiss, Geoff}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3736--3744}, 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/fan26c/fan26c.pdf}, url = {https://proceedings.mlr.press/v300/fan26c.html}, abstract = { In Bayesian optimization, Thompson sampling selects the evaluation point by sampling from the posterior distribution over the objective function maximizer. Because this sampling problem is intractable for Gaussian process (GP) surrogates, the posterior distribution is typically restricted to fixed discretizations (i.e., candidate points) that become exponentially sparse as dimensionality increases. While previous works aim to increase candidate point density through scalable GP approximations, our orthogonal approach increases density by adaptively reducing the search space during sampling. Specifically, we introduce Adaptive Candidate Thompson Sampling (ACTS), which generates candidate points in subspaces guided by the gradient of a surrogate model sample. ACTS is a simple drop-in replacement for existing TS methods—including those that use trust regions or other local approximations—producing better samples of maxima and improved optimization across synthetic and real-world benchmarks. } }
Endnote
%0 Conference Paper %T Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization %A Donney Fan %A Geoff Pleiss %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-fan26c %I PMLR %P 3736--3744 %U https://proceedings.mlr.press/v300/fan26c.html %V 300 %X In Bayesian optimization, Thompson sampling selects the evaluation point by sampling from the posterior distribution over the objective function maximizer. Because this sampling problem is intractable for Gaussian process (GP) surrogates, the posterior distribution is typically restricted to fixed discretizations (i.e., candidate points) that become exponentially sparse as dimensionality increases. While previous works aim to increase candidate point density through scalable GP approximations, our orthogonal approach increases density by adaptively reducing the search space during sampling. Specifically, we introduce Adaptive Candidate Thompson Sampling (ACTS), which generates candidate points in subspaces guided by the gradient of a surrogate model sample. ACTS is a simple drop-in replacement for existing TS methods—including those that use trust regions or other local approximations—producing better samples of maxima and improved optimization across synthetic and real-world benchmarks.
APA
Fan, D. & Pleiss, G.. (2026). Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3736-3744 Available from https://proceedings.mlr.press/v300/fan26c.html.

Related Material