# Bayesian Optimisation for Mixed-Variable Inputs using Value Proposals

arXiv: https://arxiv.org/abs/2202.04832 · HTML: https://mlsanity.com/paper/2202.04832/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [Bayesian Optimisation over Multiple Continuous and Categorical Inputs](https://mlsanity.com/paper/1906.08878/) (2019)
- [Bayesian Optimization for Categorical and Category-Specific Continuous Inputs](https://mlsanity.com/paper/1911.12473/) (2019)
- [Constrained Bayesian Optimization for Automatic Chemical Design](https://mlsanity.com/paper/1709.05501/) (2017)
- [Gaussian Process Models with Low-Rank Correlation Matrices for Both Continuous and Categorical Inputs](https://mlsanity.com/paper/2010.02574/) (2020)

## Abstract (arXiv)

Many real-world optimisation problems are defined over both categorical and continuous variables, yet efficient optimisation methods such asBayesian Optimisation (BO) are not designed tohandle such mixed-variable search spaces. Recent approaches to this problem cast the selection of the categorical variables as a bandit problem, operating independently alongside a BO component which optimises the continuous variables. In this paper, we adopt a holistic view and aim to consolidate optimisation of the categorical and continuous sub-spaces under a single acquisition metric. We derive candidates from the ExpectedImprovement criterion, which we call value proposals, and use these proposals to make selections on both the categorical and continuous components of the input. We show that this unified approach significantly outperforms existing mixed-variable optimisation approaches across several mixed-variable black-box optimisation tasks.