Can Multi-Objective Bayesian Optimisation Work Without Posterior Uncertainty?

Bayesian optimisation (BO) is a sample-efficient approach for solving expensive black-box optimisation problems. It uses a probabilistic surrogate model to provide a posterior distribution over the unknown objective function and an acquisition function to select solutions for evaluation. Acquisition functions commonly use both the model's posterior mean and posterior uncertainty to balance exploitation and exploration, favouring solutions with better predicted objective values while exploring regions where predictions are less certain. Most multi-objective Bayesian optimisation (MOBO) methods follow such a design. In this paper, we argue that it may not be necessary to consider posterior uncertainty in every MOBO design. In single-objective BO, using only the posterior mean may keep the search near the currently predicted best solution, leaving other regions unexplored. In MOBO, however, considering the posterior means across different objectives (i.e., their nondominance relations) can also facilitate exploration. Rather than focusing solely on solutions with the best posterior mean for each objective, the search can identify solutions representing different trade-offs among the objectives. These trade-off solutions may be located in different areas in the search space, allowing exploration to emerge from these areas without explicitly modelling posterior uncertainty. Based on this, we propose a simple MOBO framework that considers only the posterior means of the surrogate models. We investigate two instantiations of this framework: one directly approximates the Pareto front formed by the posterior means, while the other optimises the scalarised posterior means to learn the corresponding Pareto set. We evaluate it on a wide range of benchmark and real-world problems. The results show that it performs very competitively with state-of-the-art methods, even under noisy settings.