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

NeurIPS 2026 · Probabilistic and scientific modeling › Bayesian optimization · approach: Acquisition function design · 0 citations (OpenAlex)

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Proposes DT-PBO, an interpretable tree-based surrogate for preferential Bayesian optimization that learns shallow decision trees directly from pairwise comparisons via a consistency-score splitting heuristic and Laplace-approximated Gaussian leaves, paired with qEUBO.

Problem

Gaussian process surrogates in preferential Bayesian optimization (PBO) are black boxes, which limits interpretability and trust in high-stakes settings such as healthcare, and existing tree methods for pairwise comparison data do not support probabilistic estimates for active learning.

Approach

A greedy decision tree split heuristic (consistency score) computed directly on winner-loser pairs, with straddling pairs discarded during recursion to keep trees shallow, plus independent-normal-prior Laplace approximation over leaf values with a sum-to-zero constraint, yielding probabilistic leaves usable by qEUBO.

Key results

• On eight benchmark functions DT-PBO is competitive with GP-based PBO, outperforming GP models on De Jong, Holder and Schwefel but slightly worse on Rosenbrock and Hartmann.
• DT-PBO's running time is reported as 10-400 times faster than GP-based models.
• On the sushi dataset both GP and DT-PBO reach a test accuracy of about 0.9 and identify the most preferred sushi in under 9 questions in about 70% of cases.
• On PMR, the tree-based model achieves performance competitive with the pure LLM approach (about 0.72 reported for LLM baselines) while being interpretable.

Surprising findings

• Discarding straddling pairs during tree recursion yields much more interpretable trees while retaining nearly all test accuracy on BELA (0.63 vs 0.60 test accuracy when keeping straddlers).

Limitations

• Cannot model indifference statements (A ~ B).
• Struggles on non-rugged functions as dimensionality grows (D > 7).
• Final model quality in the PMR case depends on reliability of LLM-based feature extraction.

Experimental setup

Datasets: Sushi preference dataset PMR-Synth eight synthetic benchmark functions (Rosenbrock, Hartmann, Branin, Levy, Michalewicz, De Jong, Holder, Schwefel)

Benchmarks: Rosenbrock Hartmann Branin Levy Michalewicz De Jong Holder Schwefel Sushi PMR-Synth

Metrics: regret rho-regret top-1 rank error train/test accuracy running time

Baselines: GP-qEUBO SkewGP with HB-EI random query selection Qwen3.5-27B pure LLM Gatto et al. fine-tuned LLM

Builds on: Gaussian process preference learning qEUBO skewGP Laplace approximation

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