# Multi-objective optimisation via the R2 utilities

arXiv: https://arxiv.org/abs/2305.11774 · HTML: https://mlsanity.com/paper/2305.11774/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 106 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 23 of 23)

- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [A Survey of Multi-Objective Sequential Decision-Making](https://mlsanity.com/paper/1402.0590/) (2014)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [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)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/1609.01051/) (2016)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [Multi-Attribute Bayesian Optimization With Interactive Preference Learning](https://mlsanity.com/paper/1911.05934/) (2019)
- [Ordered Preference Elicitation Strategies for Supporting Multi-Objective Decision Making](https://mlsanity.com/paper/1802.07606/) (2018)
- [No-regret Algorithms for Multi-task Bayesian Optimization](https://mlsanity.com/paper/2008.08885/) (2020)
- [Multi-Objective Learning to Predict Pareto Fronts Using Hypervolume Maximization](https://mlsanity.com/paper/2102.04523/) (2021)
- [Scalarizing Functions in Bayesian Multiobjective Optimization](https://mlsanity.com/paper/1904.05760/) (2019)
- [The Kalai-Smorodinski solution for many-objective Bayesian optimization](https://mlsanity.com/paper/1902.06565/) (2019)
- [Noisy Submodular Maximization via Adaptive Sampling with Applications to Crowdsourced Image Collection Summarization](https://mlsanity.com/paper/1511.07211/) (2015)
- [A Bayesian optimization approach to find Nash equilibria](https://mlsanity.com/paper/1611.02440/) (2016)

## Built on by (most cited first, 3 of 3)

- [AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance](https://mlsanity.com/paper/2510.00352/) (2025)
- [Random Pareto front surfaces](https://mlsanity.com/paper/2405.01404/) (2024)
- [Scalarisation-based risk concepts for robust multi-objective optimisation](https://mlsanity.com/paper/2405.10221/) (2024)

## Abstract (arXiv)

The goal of multi-objective optimisation is to identify a collection of points which describe the best possible trade-offs between the multiple objectives. In order to solve this vector-valued optimisation problem, practitioners often appeal to the use of scalarisation functions in order to transform the multi-objective problem into a collection of single-objective problems. This set of scalarised problems can then be solved using traditional single-objective optimisation techniques. In this work, we formalise this convention into a general mathematical framework. We show how this strategy effectively recasts the original multi-objective optimisation problem into a single-objective optimisation problem defined over sets. An appropriate class of objective functions for this new problem are the R2 utilities, which are utility functions that are defined as a weighted integral over the scalarised optimisation problems. As part of our work, we show that these utilities are monotone and submodular set functions which can be optimised effectively using greedy optimisation algorithms. We then analyse the performance of these greedy algorithms both theoretically and empirically. Our analysis largely focusses on Bayesian optimisation, which is a popular probabilistic framework for black-box optimisation.