# Anchor-Based Heteroscedastic Noise for Preferential Bayesian Optimization

arXiv: https://arxiv.org/abs/2405.14657 · HTML: https://mlsanity.com/paper/2405.14657/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 14 of 14)

- [HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation](https://mlsanity.com/paper/2012.03826/) (2020)
- [Preferential Bayesian Optimization](https://mlsanity.com/paper/1704.03651/) (2017)
- [πBO: Augmenting Acquisition Functions with User Beliefs for Bayesian Optimization](https://mlsanity.com/paper/2204.11051/) (2022)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [Sequential Gallery for Interactive Visual Design Optimization](https://mlsanity.com/paper/2005.04107/) (2020)
- [qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization](https://mlsanity.com/paper/2303.15746/) (2023)
- [A General Framework for User-Guided Bayesian Optimization](https://mlsanity.com/paper/2311.14645/) (2023)
- [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)
- [Preferential Bayesian optimisation with Skew Gaussian Processes](https://mlsanity.com/paper/2008.06677/) (2020)
- [Principled Preferential Bayesian Optimization](https://mlsanity.com/paper/2402.05367/) (2024)
- [Achieving Robustness to Aleatoric Uncertainty with Heteroscedastic Bayesian Optimisation](https://mlsanity.com/paper/1910.07779/) (2019)
- [Batch Bayesian Optimization for Replicable Experimental Design](https://mlsanity.com/paper/2311.01195/) (2023)

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

- [PABBO: Preferential Amortized Black-Box Optimization](https://mlsanity.com/paper/2503.00924/) (2025)

## Abstract (arXiv)

Preferential Bayesian optimization (PBO) learns latent utilities from pairwise comparisons, but most existing methods assume homoscedastic comparison noise. This is inadequate in human-in-the-loop settings, where a user may compare some designs reliably and others only hesitantly. We propose a heteroscedastic noise model for PBO: before optimization, the user provides a small set of reliable examples, called anchors, and a kernel density estimator (KDE) turns these anchors into an input-dependent map of user uncertainty. We incorporate this map into preferential GP surrogates and derive risk-averse acquisition functions that trade off utility and ease of comparison. We further show that a risk-adjusted variant of the popular expected utility of the best option (EUBO) preserves the one-step Bayes-optimality guarantee up to an additive constant, and that under an idealized i.i.d. anchor model the KDE estimator enjoys standard consistency and concentration rates. Experiments on synthetic problems and human-preference datasets show improved risk-adjusted performance and clarify how anchor placement affects the method.