# MBORE: Multi-objective Bayesian Optimisation by Density-Ratio Estimation

arXiv: https://arxiv.org/abs/2203.16912 · HTML: https://mlsanity.com/paper/2203.16912/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 92 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 25 of 25)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [Batched High-dimensional Bayesian Optimization via Structural Kernel Learning](https://mlsanity.com/paper/1703.01973/) (2017)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Data-efficient Learning of Morphology and Controller for a Microrobot](https://mlsanity.com/paper/1905.01334/) (2019)
- [BORE: Bayesian Optimization by Density-Ratio Estimation](https://mlsanity.com/paper/2102.09009/) (2021)
- [Fast Information-theoretic Bayesian Optimisation](https://mlsanity.com/paper/1711.00673/) (2017)
- [Orthogonally Decoupled Variational Gaussian Processes](https://mlsanity.com/paper/1809.08820/) (2018)
- [Scalarizing Functions in Bayesian Multiobjective Optimization](https://mlsanity.com/paper/1904.05760/) (2019)
- [What do you Mean? The Role of the Mean Function in Bayesian Optimisation](https://mlsanity.com/paper/2004.08349/) (2020)
- [How Bayesian Should Bayesian Optimisation Be?](https://mlsanity.com/paper/2105.00894/) (2021)
- [Preselection via Classification: A Case Study on Evolutionary Multiobjective Optimization](https://mlsanity.com/paper/1708.01146/) (2017)

## Built on by (most cited first, 5 of 5)

- [Batch Bayesian optimisation via density-ratio estimation with guarantees](https://mlsanity.com/paper/2209.10715/) (2022)
- [Mono-surrogate vs Multi-surrogate in Multi-objective Bayesian Optimisation](https://mlsanity.com/paper/2208.07240/) (2022)
- [Amortized Active Generation of Pareto Sets](https://mlsanity.com/paper/2510.21052/) (2025)
- [Deterministic Langevin Unconstrained Optimization with Normalizing Flows](https://mlsanity.com/paper/2310.00745/) (2023)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)

## Abstract (arXiv)

Optimisation problems often have multiple conflicting objectives that can be computationally and/or financially expensive. Mono-surrogate Bayesian optimisation (BO) is a popular model-based approach for optimising such black-box functions. It combines objective values via scalarisation and builds a Gaussian process (GP) surrogate of the scalarised values. The location which maximises a cheap-to-query acquisition function is chosen as the next location to expensively evaluate. While BO is an effective strategy, the use of GPs is limiting. Their performance decreases as the problem input dimensionality increases, and their computational complexity scales cubically with the amount of data. To address these limitations, we extend previous work on BO by density-ratio estimation (BORE) to the multi-objective setting. BORE links the computation of the probability of improvement acquisition function to that of probabilistic classification. This enables the use of state-of-the-art classifiers in a BO-like framework. In this work we present MBORE: multi-objective Bayesian optimisation by density-ratio estimation, and compare it to BO across a range of synthetic and real-world benchmarks. We find that MBORE performs as well as or better than BO on a wide variety of problems, and that it outperforms BO on high-dimensional and real-world problems.