# Choice functions based multi-objective Bayesian optimisation

arXiv: https://arxiv.org/abs/2110.08217 · HTML: https://mlsanity.com/paper/2110.08217/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Preferential Bayesian Optimization](https://mlsanity.com/paper/1704.03651/) (2017)
- [Automatic Variational Inference in Stan](https://mlsanity.com/paper/1506.03431/) (2015)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [Preferential Batch Bayesian Optimization](https://mlsanity.com/paper/2003.11435/) (2020)
- [Preferential Bayesian optimisation with Skew Gaussian Processes](https://mlsanity.com/paper/2008.06677/) (2020)
- [Integrals over Gaussians under Linear Domain Constraints](https://mlsanity.com/paper/1910.09328/) (2019)
- [Bayesian Optimization for Multi-objective Optimization and Multi-point Search](https://mlsanity.com/paper/1905.02370/) (2019)
- [Skew Gaussian Processes for Classification](https://mlsanity.com/paper/2005.12987/) (2020)
- [A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes](https://mlsanity.com/paper/2012.06846/) (2020)
- [Learning Choice Functions via Pareto-Embeddings](https://mlsanity.com/paper/2007.06927/) (2020)

## Built on by (most cited first, 2 of 2)

- [The Impact of Expertise in the Loop for Exploring Machine Rationality](https://mlsanity.com/paper/2302.05665/) (2023)
- [Rethinking Opinion Measurement Interfaces for Human-in-the-Loop Optimization](https://mlsanity.com/paper/2610.14757/) (2026)

## Abstract (arXiv)

In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as ``I pick options A,B,C among this set of five options A,B,C,D,E''. The fact that the option D is rejected means that there is at least one option among the selected ones A,B,C that I strictly prefer over D (but I do not have to specify which one). We assume that there is a latent vector function f for some dimension ne which embeds the options into the real vector space of dimension n, so that the choice set can be represented through a Pareto set of non-dominated options. By placing a Gaussian process prior on f and deriving a novel likelihood model for choice data, we propose a Bayesian framework for choice functions learning. We then apply this surrogate model to solve a novel multi-objective Bayesian optimisation from choice data problem.