# Ordinal Bayesian Optimisation

arXiv: https://arxiv.org/abs/1912.02493 · HTML: https://mlsanity.com/paper/1912.02493/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [Optimal Order Simple Regret for Gaussian Process Bandits](https://mlsanity.com/paper/2108.09262/) (2021)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization](https://mlsanity.com/paper/2206.03034/) (2022)
- [Modular Jump Gaussian Processes](https://mlsanity.com/paper/2505.15557/) (2025)
- [From Automation to Autonomy in Smart Manufacturing: A Bayesian Optimization Framework for Modeling Multi-Objective Experimentation and Sequential Decision Making](https://mlsanity.com/paper/2504.04244/) (2025)
- [Density Ratio Estimation-based Bayesian Optimization with Semi-Supervised Learning](https://mlsanity.com/paper/2305.15612/) (2023)
- [Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2605.20145/) (2026)

## Abstract (arXiv)

Bayesian optimisation is a powerful tool to solve expensive black-box problems, but fails when the stationary assumption made on the objective function is strongly violated, which is the case in particular for ill-conditioned or discontinuous objectives. We tackle this problem by proposing a new Bayesian optimisation framework that only considers the ordering of variables, both in the input and output spaces, to fit a Gaussian process in a latent space. By doing so, our approach is agnostic to the original metrics on the original spaces. We propose two algorithms, respectively based on an optimistic strategy and on Thompson sampling. For the optimistic strategy we prove an optimal performance under the measure of regret in the latent space. We illustrate the capability of our framework on several challenging toy problems.