# Bayesian Optimization for Multi-objective Optimization and Multi-point Search

arXiv: https://arxiv.org/abs/1905.02370 · HTML: https://mlsanity.com/paper/1905.02370/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2019.

## Built on by (most cited first, 8 of 8)

- [BOFormer: Learning to Solve Multi-Objective Bayesian Optimization via Non-Markovian RL](https://mlsanity.com/paper/2505.21974/) (2025)
- [PropertyDAG: Multi-objective Bayesian optimization of partially ordered, mixed-variable properties for biological sequence design](https://mlsanity.com/paper/2210.04096/) (2022)
- [Towards Leveraging AutoML for Sustainable Deep Learning: A Multi-Objective HPO Approach on Deep Shift Neural Networks](https://mlsanity.com/paper/2404.01965/) (2024)
- [Choice functions based multi-objective Bayesian optimisation](https://mlsanity.com/paper/2110.08217/) (2021)
- [FoMEMO: Towards Foundation Models for Expensive Multi-objective Optimization](https://mlsanity.com/paper/2509.03244/) (2025)
- [RIBBON: Cost-Effective and QoS-Aware Deep Learning Model Inference using a Diverse Pool of Cloud Computing Instances](https://mlsanity.com/paper/2207.11434/) (2022)
- [Leveraging AutoML for Sustainable Deep Learning: A Multi-Objective HPO Approach on Deep Shift Neural Networks](https://mlsanity.com/paper/2606.23208/) (2026)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)

## Abstract (arXiv)

Bayesian optimization is an effective method to efficiently optimize unknown objective functions with high evaluation costs. Traditional Bayesian optimization algorithms select one point per iteration for single objective function, whereas in recent years, Bayesian optimization for multi-objective optimization or multi-point search per iteration have been proposed. However, Bayesian optimization that can deal with them at the same time in non-heuristic way is not known at present. We propose a Bayesian optimization algorithm that can deal with multi-objective optimization and multi-point search at the same time. First, we define an acquisition function that considers both multi-objective and multi-point search problems. It is difficult to analytically maximize the acquisition function as the computational cost is prohibitive even when approximate calculations such as sampling approximation are performed; therefore, we propose an accurate and computationally efficient method for estimating gradient of the acquisition function, and develop an algorithm for Bayesian optimization with multi-objective and multi-point search. It is shown via numerical experiments that the performance of the proposed method is comparable or superior to those of heuristic methods.