# qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization

arXiv: https://arxiv.org/abs/2303.15746 · HTML: https://mlsanity.com/paper/2303.15746/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 28 Mar 2023.

## Builds on (most cited first, 16 of 16)

- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Preference-based Online Learning with Dueling Bandits: A Survey](https://mlsanity.com/paper/1807.11398/) (2018)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Preferential Bayesian Optimization](https://mlsanity.com/paper/1704.03651/) (2017)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Parallel Bayesian Global Optimization of Expensive Functions](https://mlsanity.com/paper/1602.05149/) (2016)
- [Double Thompson Sampling for Dueling Bandits](https://mlsanity.com/paper/1604.07101/) (2016)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Preference-Based Learning for Exoskeleton Gait Optimization](https://mlsanity.com/paper/1909.12316/) (2019)
- [Projective Preferential Bayesian Optimization](https://mlsanity.com/paper/2002.03113/) (2020)
- [Top-k Ranking Bayesian Optimization](https://mlsanity.com/paper/2012.10688/) (2020)
- [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)
- [Adaptive Nonparametric Psychophysics](https://mlsanity.com/paper/2104.09549/) (2021)

## Built on by (most cited first, 23 of 23)

- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [Principled Preferential Bayesian Optimization](https://mlsanity.com/paper/2402.05367/) (2024)
- [PABBO: Preferential Amortized Black-Box Optimization](https://mlsanity.com/paper/2503.00924/) (2025)
- [Principled Bayesian Optimisation in Collaboration with Human Experts](https://mlsanity.com/paper/2410.10452/) (2024)
- [Preferential Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2406.14699/) (2024)
- [Cold-Start Personalization via Training-Free Priors from Structured World Models](https://mlsanity.com/paper/2602.15012/) (2026)
- [Bayesian preference elicitation for decision support in multiobjective optimization](https://mlsanity.com/paper/2507.16999/) (2025)
- [Anchor-Based Heteroscedastic Noise for Preferential Bayesian Optimization](https://mlsanity.com/paper/2405.14657/) (2024)
- [Bayesian Optimization with Preference Exploration using a Monotonic Neural Network Ensemble](https://mlsanity.com/paper/2501.18792/) (2025)
- [Preferential Multi-Objective Bayesian Optimization for Drug Discovery](https://mlsanity.com/paper/2503.16841/) (2025)
- [An Interactive Framework for Finding the Optimal Trade-off in Differential Privacy](https://mlsanity.com/paper/2509.04290/) (2025)
- [Knowledge Gradient for Preference Learning](https://mlsanity.com/paper/2601.22335/) (2026)
- [Efficient Controller Learning from Human Preferences and Numerical Data Via Multi-Modal Surrogate Models](https://mlsanity.com/paper/2603.24138/) (2026)
- [Direct Preference-Based Evolutionary Multi-Objective Optimization with Dueling Bandit](https://mlsanity.com/paper/2311.14003/) (2023)
- [BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization](https://mlsanity.com/paper/2508.02332/) (2025)
- [Consecutive Preferential Bayesian Optimization](https://mlsanity.com/paper/2511.05163/) (2025)
- [DT-PBO: an Interpretable Tree-based Surrogate Model for Preferential Bayesian Optimization](https://mlsanity.com/paper/2512.14263/) (2025)
- [Vibrotactile Preference Learning: Uncertainty-Aware Preference Learning for Personalized Vibration Feedback](https://mlsanity.com/paper/2604.20210/) (2026)
- [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)
- [Eliciting ESG Preferences for Reinforcement Learning-Based Portfolio Optimization](https://mlsanity.com/paper/2609.02677/) (2026)

## Abstract (arXiv)

Preferential Bayesian optimization (PBO) is a framework for optimizing a decision maker's latent utility function using preference feedback. This work introduces the expected utility of the best option (qEUBO) as a novel acquisition function for PBO. When the decision maker's responses are noise-free, we show that qEUBO is one-step Bayes optimal and thus equivalent to the popular knowledge gradient acquisition function. We also show that qEUBO enjoys an additive constant approximation guarantee to the one-step Bayes-optimal policy when the decision maker's responses are corrupted by noise. We provide an extensive evaluation of qEUBO and demonstrate that it outperforms the state-of-the-art acquisition functions for PBO across many settings. Finally, we show that, under sufficient regularity conditions, qEUBO's Bayesian simple regret converges to zero at a rate o(1/n) as the number of queries, n, goes to infinity. In contrast, we show that simple regret under qEI, a popular acquisition function for standard BO often used for PBO, can fail to converge to zero. Enjoying superior performance, simple computation, and a grounded decision-theoretic justification, qEUBO is a promising acquisition function for PBO.