# Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisation

arXiv: https://arxiv.org/abs/2006.04296 · HTML: https://mlsanity.com/paper/2006.04296/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 22 of 22)

- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds](https://mlsanity.com/paper/2302.01511/) (2023)
- [Predicate Invention by Learning From Failures](https://mlsanity.com/paper/2104.14426/) (2021)
- [Learning logic programs by combining programs](https://mlsanity.com/paper/2206.01614/) (2022)
- [Generalisation Through Negation and Predicate Invention](https://mlsanity.com/paper/2301.07629/) (2023)
- [EXPIL: Explanatory Predicate Invention for Learning in Games](https://mlsanity.com/paper/2406.06107/) (2024)
- [Learning logic programs by discovering where not to search](https://mlsanity.com/paper/2202.09806/) (2022)
- [Regret Analysis for Randomized Gaussian Process Upper Confidence Bound](https://mlsanity.com/paper/2409.00979/) (2024)
- [Online inductive learning from answer sets for efficient reinforcement learning exploration](https://mlsanity.com/paper/2501.07445/) (2025)
- [Mastering the exploration-exploitation trade-off in Bayesian Optimization](https://mlsanity.com/paper/2305.08624/) (2023)
- [Active Learning for Level Set Estimation Using Randomized Straddle Algorithms](https://mlsanity.com/paper/2408.03144/) (2024)
- [Robust Bayesian optimization with reinforcement learned acquisition functions](https://mlsanity.com/paper/2210.00476/) (2022)
- [Wasserstein Barycenter Gaussian Process based Bayesian Optimization](https://mlsanity.com/paper/2505.12471/) (2025)
- [Uncertainty quantification and exploration-exploitation trade-off in humans](https://mlsanity.com/paper/2102.07647/) (2021)
- [Atlas: Automate Online Service Configuration in Network Slicing](https://mlsanity.com/paper/2210.16902/) (2022)
- [Scalable Knowledge Refactoring using Constrained Optimisation](https://mlsanity.com/paper/2408.11530/) (2024)
- [A Unified Batch Selection Policy for Active Metric Learning](https://mlsanity.com/paper/2102.07365/) (2021)
- [Learning logic programs by explaining their failures](https://mlsanity.com/paper/2102.12551/) (2021)
- [BORA: Bayesian Optimization for Resource Allocation](https://mlsanity.com/paper/2210.05977/) (2022)
- [An Empirical Comparison of Cost Functions in Inductive Logic Programming](https://mlsanity.com/paper/2503.07554/) (2025)
- [Honey, I shrunk the hypothesis space (through logical preprocessing)](https://mlsanity.com/paper/2506.06739/) (2025)

## Abstract (arXiv)

In order to improve the performance of Bayesian optimisation, we develop a modified Gaussian process upper confidence bound (GP-UCB) acquisition function. This is done by sampling the exploration-exploitation trade-off parameter from a distribution. We prove that this allows the expected trade-off parameter to be altered to better suit the problem without compromising a bound on the function's Bayesian regret. We also provide results showing that our method achieves better performance than GP-UCB in a range of real-world and synthetic problems.