# Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling

arXiv: https://arxiv.org/abs/2502.01226 · HTML: https://mlsanity.com/paper/2502.01226/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 53 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 29 of 29)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [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)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space](https://mlsanity.com/paper/1706.01825/) (2017)
- [Meta-Thompson Sampling](https://mlsanity.com/paper/2102.06129/) (2021)
- [No-Regret Bayesian Optimization with Unknown Hyperparameters](https://mlsanity.com/paper/1901.03357/) (2019)
- [Time-Varying Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1601.06650/) (2016)
- [Regret Bound Balancing and Elimination for Model Selection in Bandits and RL](https://mlsanity.com/paper/2012.13045/) (2020)
- [Efficient Learning in Large-Scale Combinatorial Semi-Bandits](https://mlsanity.com/paper/1406.7443/) (2014)
- [Hierarchical Bayesian Bandits](https://mlsanity.com/paper/2111.06929/) (2021)
- [Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters](https://mlsanity.com/paper/1406.7758/) (2014)
- [No Regrets for Learning the Prior in Bandits](https://mlsanity.com/paper/2107.06196/) (2021)
- [Surrogate modeling for Bayesian optimization beyond a single Gaussian process](https://mlsanity.com/paper/2205.14090/) (2022)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [Tight Regret Bounds for Bayesian Optimization in One Dimension](https://mlsanity.com/paper/1805.11792/) (2018)
- [Regret Balancing for Bandit and RL Model Selection](https://mlsanity.com/paper/2006.05491/) (2020)
- [Thompson Sampling with a Mixture Prior](https://mlsanity.com/paper/2106.05608/) (2021)
- [Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds](https://mlsanity.com/paper/2311.03760/) (2023)
- [Financial Applications of Gaussian Processes and Bayesian Optimization](https://mlsanity.com/paper/1903.04841/) (2019)
- [Time-Varying Gaussian Process Bandits with Unknown Prior](https://mlsanity.com/paper/2402.01632/) (2024)
- [Online Learning of Network Bottlenecks via Minimax Paths](https://mlsanity.com/paper/2109.08467/) (2021)
- [Online Learning of Energy Consumption for Navigation of Electric Vehicles](https://mlsanity.com/paper/2111.02314/) (2021)
- [Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimal](https://mlsanity.com/paper/2410.10384/) (2024)
- [How Bayesian Should Bayesian Optimisation Be?](https://mlsanity.com/paper/2105.00894/) (2021)
- [Bayesian Analysis of Combinatorial Gaussian Process Bandits](https://mlsanity.com/paper/2312.12676/) (2023)
- [Modified Meta-Thompson Sampling for Linear Bandits and Its Bayes Regret Analysis](https://mlsanity.com/paper/2409.06329/) (2024)

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

- [Online Adaptive Kernel Mixing for Gaussian Process Decision Making](https://mlsanity.com/paper/2609.19891/) (2026)
- [Bayesian Optimization of CVaR with Unknown Hyperparameters](https://mlsanity.com/paper/2610.18306/) (2026)

## Abstract (arXiv)

Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions. The characteristics of the unknown function depend heavily on the assumed GP prior. Most work in the literature assume that this prior is known but in practice this seldom holds. Instead, practitioners often rely on maximum likelihood estimation to select the hyperparameters of the prior - which lacks theoretical guarantees. In this work, we study two algorithms for joint prior selection and regret minimization in GP bandits based on GP Thompson sampling (GP-TS): Prior-Elimination GP-TS (PE-GP-TS) that disqualifies priors with poor predictive performance, and HyperPrior GP-TS (HP-GP-TS) that utilizes a bi-level Thompson sampling scheme. We theoretically analyze the algorithms and establish a sublinear regret bound for HP-GP-TS. In addition, we demonstrate the effectiveness of these algorithms compared to the alternatives through extensive experiments with synthetic and real-world data.