# Bayesian Optimization with Preference Exploration using a Monotonic Neural Network Ensemble

arXiv: https://arxiv.org/abs/2501.18792 · HTML: https://mlsanity.com/paper/2501.18792/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 57 references that are in the map.
- First posted on arXiv 30 Jan 2025.

## Builds on (most cited first, 29 of 29)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search](https://mlsanity.com/paper/1910.11858/) (2019)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Preferential Bayesian Optimization](https://mlsanity.com/paper/1704.03651/) (2017)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [BOCK : Bayesian Optimization with Cylindrical Kernels](https://mlsanity.com/paper/1806.01619/) (2018)
- [A Study of Bayesian Neural Network Surrogates for Bayesian Optimization](https://mlsanity.com/paper/2305.20028/) (2023)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [GradDiv: Adversarial Robustness of Randomized Neural Networks via Gradient Diversity Regularization](https://mlsanity.com/paper/2107.02425/) (2021)
- [Computer-Aided Multi-Objective Optimization in Small Molecule Discovery](https://mlsanity.com/paper/2210.07209/) (2022)
- [qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization](https://mlsanity.com/paper/2303.15746/) (2023)
- [Projective Preferential Bayesian Optimization](https://mlsanity.com/paper/2002.03113/) (2020)
- [Multi-Attribute Bayesian Optimization With Interactive Preference Learning](https://mlsanity.com/paper/1911.05934/) (2019)
- [Preferential Batch Bayesian Optimization](https://mlsanity.com/paper/2003.11435/) (2020)
- [Towards Practical Preferential Bayesian Optimization with Skew Gaussian Processes](https://mlsanity.com/paper/2302.01513/) (2023)
- [Principled Preferential Bayesian Optimization](https://mlsanity.com/paper/2402.05367/) (2024)
- [Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structure](https://mlsanity.com/paper/2104.11667/) (2021)
- [Multi-Objective Bayesian Optimization with Active Preference Learning](https://mlsanity.com/paper/2311.13460/) (2023)
- [Skew Gaussian Processes for Classification](https://mlsanity.com/paper/2005.12987/) (2020)
- [High-dimensional additive Gaussian processes under monotonicity constraints](https://mlsanity.com/paper/2205.08528/) (2022)
- [Enhanced Bayesian Optimization via Preferential Modeling of Abstract Properties](https://mlsanity.com/paper/2402.17343/) (2024)
- [Preferential Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2406.14699/) (2024)

## Built on by (most cited first, 1 of 1)

- [Conditioning Gaussian Processes on Almost Anything](https://mlsanity.com/paper/2605.21041/) (2026)

## Abstract (arXiv)

Many real-world black-box optimization problems have multiple conflicting objectives. Rather than attempting to approximate the entire set of Pareto-optimal solutions, interactive preference learning allows to focus the search on the most relevant subset. However, few previous studies have exploited the fact that utility functions are usually monotonic. In this paper, we address the Bayesian Optimization with Preference Exploration (BOPE) problem and propose using a neural network ensemble as a utility surrogate model. This approach naturally integrates monotonicity and supports pairwise comparison data. Our experiments demonstrate that the proposed method outperforms state-of-the-art approaches and exhibits robustness to noise in utility evaluations. An ablation study highlights the critical role of monotonicity in enhancing performance.