# Gaussian Process Thompson Sampling via Rootfinding

arXiv: https://arxiv.org/abs/2410.08071 · HTML: https://mlsanity.com/paper/2410.08071/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space](https://mlsanity.com/paper/1706.01825/) (2017)
- [Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functions](https://mlsanity.com/paper/1511.07130/) (2015)

## Built on by (most cited first, 2 of 2)

- [Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization](https://mlsanity.com/paper/2410.23482/) (2024)
- [Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimization](https://mlsanity.com/paper/2507.14746/) (2025)

## Abstract (arXiv)

Thompson sampling (TS) is a simple, effective stochastic policy in Bayesian decision making. It samples the posterior belief about the reward profile and optimizes the sample to obtain a candidate decision. In continuous optimization, the posterior of the objective function is often a Gaussian process (GP), whose sample paths have numerous local optima, making their global optimization challenging. In this work, we introduce an efficient global optimization strategy for GP-TS that carefully selects starting points for gradient-based multi-start optimizers. It identifies all local optima of the prior sample via univariate global rootfinding, and optimizes the posterior sample using a differentiable, decoupled representation. We demonstrate remarkable improvement in the global optimization of GP posterior samples, especially in high dimensions. This leads to dramatic improvements in the overall performance of Bayesian optimization using GP-TS acquisition functions, surprisingly outperforming alternatives like GP-UCB and EI.