A Flexible Multi-Objective Bayesian Optimization Approach using Random Scalarizations.

Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the evaluation of the functions in question are expensive. Traditional methods for multi-objective optimization, both Bayesian and otherwise, are aimed at recovering the Pareto front of these objectives. However, we argue that recovering the entire Pareto front may not be aligned with our goals in practice. For example, while a practitioner might desire to identify Pareto optimal points, she may wish to focus only on a particular region of the Pareto front due to external considerations. In this work we propose an approach based on random scalarizations of the objectives. We demonstrate that our approach can focus its sampling on certain regions of the Pareto front while being flexible enough to sample from the entire Pareto front if required. Furthermore, our approach is less computationally demanding compared to other existing approaches. In this paper, we also analyse a notion of regret in the multi-objective setting and obtain sublinear regret bounds. We compare the proposed approach to other state-of-the-art approaches on both synthetic and real-life experiments. The results demonstrate superior performance of our proposed algorithm in terms of flexibility, scalability and regret.