# Multi-objective Bayesian optimisation with preferences over objectives

arXiv: https://arxiv.org/abs/1902.04228 · HTML: https://mlsanity.com/paper/1902.04228/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2019.

## Built on by (most cited first, 16 of 16)

- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview](https://mlsanity.com/paper/2206.07438/) (2022)
- [A survey on multi-objective hyperparameter optimization algorithms for Machine Learning](https://mlsanity.com/paper/2111.13755/) (2021)
- [Refined Coreset Selection: Towards Minimal Coreset Size under Model Performance Constraints](https://mlsanity.com/paper/2311.08675/) (2023)
- [Multi-Objective Bayesian Optimization with Active Preference Learning](https://mlsanity.com/paper/2311.13460/) (2023)
- [Preference-Aware Constrained Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2303.13034/) (2023)
- [Bayesian preference elicitation for decision support in multiobjective optimization](https://mlsanity.com/paper/2507.16999/) (2025)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [A Nested Weighted Tchebycheff Multi-Objective Bayesian Optimization Approach for Flexibility of Unknown Utopia Estimation in Expensive Black-box Design Problems](https://mlsanity.com/paper/2110.11070/) (2021)
- [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)
- [Experience in Engineering Complex Systems: Active Preference Learning with Multiple Outcomes and Certainty Levels](https://mlsanity.com/paper/2302.14630/) (2023)
- [Vector Optimization with Gaussian Process Bandits](https://mlsanity.com/paper/2412.02484/) (2024)
- [Multi-Objective Bayesian Optimization via Adaptive varepsilon-Constraints Decomposition](https://mlsanity.com/paper/2604.15959/) (2026)
- [Selective Ensemble Based on Preference-Directed Multi-Objective Bandits](https://mlsanity.com/paper/2606.21929/) (2026)

## Abstract (arXiv)

We present a multi-objective Bayesian optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type "objective A is more important than objective B". These preferences are defined based on the stability of the obtained solutions with respect to preferred objective functions. Rather than attempting to find a representative subset of the complete Pareto front, our algorithm selects those Pareto-optimal points that satisfy these constraints. We formulate a new acquisition function based on expected improvement in dominated hypervolume (EHI) to ensure that the subset of Pareto front satisfying the constraints is thoroughly explored. The hypervolume calculation is weighted by the probability of a point satisfying the constraints from a gradient Gaussian Process model. We demonstrate our algorithm on both synthetic and real-world problems.