Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisation

TL;DR

This paper introduces a modified GP-UCB acquisition function for Bayesian optimization that samples the exploration-exploitation parameter from a distribution, improving performance without losing theoretical guarantees.

Contribution

The paper proposes a novel sampling-based modification to GP-UCB that enhances optimization performance while maintaining regret bounds.

Findings

Achieves better performance than standard GP-UCB in various problems.

Maintains theoretical Bayesian regret bounds.

Effective in both real-world and synthetic scenarios.

Abstract

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.