# Projective Preferential Bayesian Optimization

arXiv: https://arxiv.org/abs/2002.03113 · HTML: https://mlsanity.com/paper/2002.03113/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2020.

## Built on by (most cited first, 22 of 22)

- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization](https://mlsanity.com/paper/2303.15746/) (2023)
- [Principled Preferential Bayesian Optimization](https://mlsanity.com/paper/2402.05367/) (2024)
- [Bandits with Preference Feedback: A Stackelberg Game Perspective](https://mlsanity.com/paper/2406.16745/) (2024)
- [Toward AI Assistants That Let Designers Design](https://mlsanity.com/paper/2107.13074/) (2021)
- [Bayesian Optimization Augmented with Actively Elicited Expert Knowledge](https://mlsanity.com/paper/2208.08742/) (2022)
- [Principled Bayesian Optimisation in Collaboration with Human Experts](https://mlsanity.com/paper/2410.10452/) (2024)
- [On Preference Learning Based on Sequential Bayesian Optimization with Pairwise Comparison](https://mlsanity.com/paper/2103.13192/) (2021)
- [Enhanced Bayesian Optimization via Preferential Modeling of Abstract Properties](https://mlsanity.com/paper/2402.17343/) (2024)
- [Cooperative Bayesian Optimization for Imperfect Agents](https://mlsanity.com/paper/2403.04442/) (2024)
- [Bayesian Optimization from Human Feedback: Near-Optimal Regret Bounds](https://mlsanity.com/paper/2505.23673/) (2025)
- [BioBO: Biology-informed Bayesian Optimization for Perturbation Design](https://mlsanity.com/paper/2509.19988/) (2025)
- [The Impact of Expertise in the Loop for Exploring Machine Rationality](https://mlsanity.com/paper/2302.05665/) (2023)
- [Bayesian Optimization with Preference Exploration using a Monotonic Neural Network Ensemble](https://mlsanity.com/paper/2501.18792/) (2025)
- [Knowledge Gradient for Preference Learning](https://mlsanity.com/paper/2601.22335/) (2026)
- [Poisson Process for Bayesian Optimization](https://mlsanity.com/paper/2402.02687/) (2024)
- [Consecutive Preferential Bayesian Optimization](https://mlsanity.com/paper/2511.05163/) (2025)
- [A Finite Time Analysis of Thompson Sampling for Bayesian Optimization with Preferential Feedback](https://mlsanity.com/paper/2604.25025/) (2026)
- [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)
- [Rethinking Opinion Measurement Interfaces for Human-in-the-Loop Optimization](https://mlsanity.com/paper/2610.14757/) (2026)

## Abstract (arXiv)

Bayesian optimization is an effective method for finding extrema of a black-box function. We propose a new type of Bayesian optimization for learning user preferences in high-dimensional spaces. The central assumption is that the underlying objective function cannot be evaluated directly, but instead a minimizer along a projection can be queried, which we call a projective preferential query. The form of the query allows for feedback that is natural for a human to give, and which enables interaction. This is demonstrated in a user experiment in which the user feedback comes in the form of optimal position and orientation of a molecule adsorbing to a surface. We demonstrate that our framework is able to find a global minimum of a high-dimensional black-box function, which is an infeasible task for existing preferential Bayesian optimization frameworks that are based on pairwise comparisons.