Anchor-Based Heteroscedastic Noise for Preferential Bayesian Optimization

Abstract

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.