Trading Off Quality and Uncertainty Through Multi-Objective Optimisation in Batch Bayesian Optimisation

Batch Bayesian Optimisation (BBO) has emerged as a potent approach for optimising expensive black-box functions. Central to BBO is the issue of selecting a number of solutions at the same time through a batch method, in the hope for them to represent good, yet different, trade-offs between exploitation and exploration. To address this issue, one of the recent advancements has leveraged multi-objective optimisation to simultaneously consider several acquisition functions (e.g., PI, EI, and LCB), allowing them to complement each other. However, acquisition functions may behave similarly (since they all aim for a good balance between exploitation and exploration), restricting the search on different promising areas. In this paper, we attempt to address the above issue. We directly treat exploitation (reflected by quality, i.e., the posterior mean) and exploration (reflected by uncertainty) as two objectives. When selecting trade-off solutions between the two objectives, we consider a dynamically updated Pareto front where the uncertainty changes once a solution is selected, thereby allowing exploration on different promising areas. Through an extensive experiment study, we show the effectiveness of the proposed method in comparison with state-of-the-arts in the area.