# Preferential Bayesian optimisation with Skew Gaussian Processes

arXiv: https://arxiv.org/abs/2008.06677 · HTML: https://mlsanity.com/paper/2008.06677/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2020.

## Built on by (most cited first, 18 of 18)

- [qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization](https://mlsanity.com/paper/2303.15746/) (2023)
- [Towards Practical Preferential Bayesian Optimization with Skew Gaussian Processes](https://mlsanity.com/paper/2302.01513/) (2023)
- [Human-in-the-Loop Optimization for Deep Stimulus Encoding in Visual Prostheses](https://mlsanity.com/paper/2306.13104/) (2023)
- [Efficient Exploration in Binary and Preferential Bayesian Optimization](https://mlsanity.com/paper/2110.09361/) (2021)
- [Learning Choice Functions with Gaussian Processes](https://mlsanity.com/paper/2302.00406/) (2023)
- [Bayesian Optimisation for Sequential Experimental Design with Applications in Additive Manufacturing](https://mlsanity.com/paper/2107.12809/) (2021)
- [GLISp-r: A preference-based optimization algorithm with convergence guarantees](https://mlsanity.com/paper/2202.01125/) (2022)
- [Enhanced Bayesian Optimization via Preferential Modeling of Abstract Properties](https://mlsanity.com/paper/2402.17343/) (2024)
- [LITE: Efficiently Estimating Gaussian Probability of Maximality](https://mlsanity.com/paper/2501.13535/) (2025)
- [Choice functions based multi-objective Bayesian optimisation](https://mlsanity.com/paper/2110.08217/) (2021)
- [Anchor-Based Heteroscedastic Noise for Preferential Bayesian Optimization](https://mlsanity.com/paper/2405.14657/) (2024)
- [Knowledge Gradient for Preference Learning](https://mlsanity.com/paper/2601.22335/) (2026)
- [A unified surrogate-based scheme for black-box and preference-based optimization](https://mlsanity.com/paper/2202.01468/) (2022)
- [The AI off-switch problem as a signalling game: bounded rationality and incomparability](https://mlsanity.com/paper/2502.06403/) (2025)
- [DT-PBO: an Interpretable Tree-based Surrogate Model for Preferential Bayesian Optimization](https://mlsanity.com/paper/2512.14263/) (2025)
- [Elicitation-Augmented Bayesian Optimization](https://mlsanity.com/paper/2605.12079/) (2026)
- [Local Preferential Bayesian Optimization](https://mlsanity.com/paper/2606.02351/) (2026)
- [Adaptive KappaSharp: Condition-Number Shaping for Preferential Bayesian Optimization](https://mlsanity.com/paper/2608.07859/) (2026)

## Abstract (arXiv)

Preferential Bayesian optimisation (PBO) deals with optimisation problems where the objective function can only be accessed via preference judgments, such as "this is better than that" between two candidate solutions (like in A/B tests or recommender systems). The state-of-the-art approach to PBO uses a Gaussian process to model the preference function and a Bernoulli likelihood to model the observed pairwise comparisons. Laplace's method is then employed to compute posterior inferences and, in particular, to build an appropriate acquisition function. In this paper, we prove that the true posterior distribution of the preference function is a Skew Gaussian Process (SkewGP), with highly skewed pairwise marginals and, thus, show that Laplace's method usually provides a very poor approximation. We then derive an efficient method to compute the exact SkewGP posterior and use it as surrogate model for PBO employing standard acquisition functions (Upper Credible Bound, etc.). We illustrate the benefits of our exact PBO-SkewGP in a variety of experiments, by showing that it consistently outperforms PBO based on Laplace's approximation both in terms of convergence speed and computational time. We also show that our framework can be extended to deal with mixed preferential-categorical BO, where binary judgments (valid or non-valid) together with preference judgments are available.