# DT-PBO: an Interpretable Tree-based Surrogate Model for Preferential Bayesian Optimization

arXiv: https://arxiv.org/abs/2512.14263 · HTML: https://mlsanity.com/paper/2512.14263/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 20 of 20)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Preference-based Online Learning with Dueling Bandits: A Survey](https://mlsanity.com/paper/1807.11398/) (2018)
- [Preferential Bayesian Optimization](https://mlsanity.com/paper/1704.03651/) (2017)
- [Reducing Dueling Bandits to Cardinal Bandits](https://mlsanity.com/paper/1405.3396/) (2014)
- [Bayesian Optimisation over Multiple Continuous and Categorical Inputs](https://mlsanity.com/paper/1906.08878/) (2019)
- [Stochastic Contextual Dueling Bandits under Linear Stochastic Transitivity Models](https://mlsanity.com/paper/2202.04593/) (2022)
- [Multi-dueling Bandits with Dependent Arms](https://mlsanity.com/paper/1705.00253/) (2017)
- [Feel-Good Thompson Sampling for Contextual Dueling Bandits](https://mlsanity.com/paper/2404.06013/) (2024)
- [qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization](https://mlsanity.com/paper/2303.15746/) (2023)
- [Top-k Ranking Bayesian Optimization](https://mlsanity.com/paper/2012.10688/) (2020)
- [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)
- [Ordered Preference Elicitation Strategies for Supporting Multi-Objective Decision Making](https://mlsanity.com/paper/1802.07606/) (2018)
- [Preferential Bayesian optimisation with Skew Gaussian Processes](https://mlsanity.com/paper/2008.06677/) (2020)
- [Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI Collaboration](https://mlsanity.com/paper/2403.04629/) (2024)
- [Efficient Exploration in Binary and Preferential Bayesian Optimization](https://mlsanity.com/paper/2110.09361/) (2021)
- [A tutorial on learning from preferences and choices with Gaussian Processes](https://mlsanity.com/paper/2403.11782/) (2024)
- [Certified Global Minima for a Benchmark of Difficult Optimization Problems](https://mlsanity.com/paper/2003.09867/) (2020)
- [Comparative Explanations: Explanation Guided Decision Making for Human-in-the-Loop Preference Selection](https://mlsanity.com/paper/2504.03744/) (2025)

## Abstract (arXiv)

Preferential Bayesian Optimization (PBO) aims to find a decision-maker's most preferred solution in as few pairwise comparisons as possible. Existing approaches rely on Gaussian Process (GP) surrogates, which provide strong performance but limited interpretability. This limits real-world usability in high-stakes domains, such as healthcare, where interpretability and trust are essential. We propose DT-PBO, a novel tree-based surrogate model for PBO that is inherently interpretable while capturing preference uncertainty. Specifically, we introduce a novel splitting heuristic that constructs interpretable shallow decision trees directly from pairwise comparison data, and use Laplace approximation to obtain probabilistic estimates for each leaf. This enables efficient preference modeling without sacrificing interpretability. Across eight benchmark functions, our method achieves competitive convergence to GP-based PBO, particularly on functions with rugged optimization landscapes. Additional experiments show robustness against noise and a fast computational running time. Experiments on real-world datasets further demonstrate that our model provides interpretable insights into decision-maker preferences that would remain opaque under GP-based approaches.