Exploration enhanced expected improvement for Bayesian optimization

Bayesian optimization (BO) is a sample-efficient method for global optimization of expensive, noisy, black-box functions using probabilistic methods. The performance of a BO method depends on its selection strategy through an acquisition function. This must balance improving our understanding of the function in unknown regions (exploration) with locally improving on known promising samples (exploitation). Expected improvement (EI) is one of the most widely used acquisition functions for BO. Unfortunately, it has a tendency to over-exploit, meaning that it can be slow in finding new peaks. We propose a modification to EI that will allow for increased early exploration while providing similar exploitation once the system has been suitably explored. We also prove that our method has a sub-linear convergence rate and test it on a range of functions to compare its performance against the standard EI and other competing methods. Code related to this paper is available at: https://github.com/jmaberk/BO_with_E3I.