Multi-Objectivising Acquisition Functions in Bayesian Optimisation

Bayesian optimisation (BO) is an efficient approach for solving expensive optimisation problems, where acquisition functions play a major role in achieving the trade-off between exploitation and exploration. The exploitation-exploration trade-off is challenging; excessive focus on exploitation can stagnate the search, while too much exploration can slow convergence. Multi-objectivisation has been explored as an effective approach to mitigate the exploitation-exploration trade-off problem. Along this line, in this paper, we propose a Multi-Objectivisation-based adaptive Exploitation-Exploration trade-off framework (MOEE) to balance exploitation and exploration in BO. MOEE considers the nondominated front formed by the exploitation and exploration objectives and adaptively switches the focus on exploration and exploitation on the basis of the search status. We verify our method on the 19 synthetic and practical problem instances with 1 to 20 dimensions, and the results show that our proposed multi-objectivisation framework can achieve a good balance between exploitation and exploration.