Preferential Bayesian optimisation with Skew Gaussian Processes

TL;DR

This paper introduces an exact Skew Gaussian Process model for Preferential Bayesian Optimisation, demonstrating improved convergence and computational efficiency over traditional Laplace approximation methods.

Contribution

It derives an exact SkewGP posterior for preference functions and applies it to Bayesian optimisation, outperforming Laplace-based methods in speed and accuracy.

Findings

SkewGP provides a more accurate posterior than Laplace approximation.

Exact SkewGP-based PBO outperforms Laplace-based PBO in experiments.

Framework extends to mixed preference and categorical judgments.

Abstract

Preferential Bayesian optimisation (PBO) deals with optimisation problems where the objective function can only be accessed via preference judgments, such as "this is better than that" between two candidate solutions (like in A/B tests or recommender systems). The state-of-the-art approach to PBO uses a Gaussian process to model the preference function and a Bernoulli likelihood to model the observed pairwise comparisons. Laplace's method is then employed to compute posterior inferences and, in particular, to build an appropriate acquisition function. In this paper, we prove that the true posterior distribution of the preference function is a Skew Gaussian Process (SkewGP), with highly skewed pairwise marginals and, thus, show that Laplace's method usually provides a very poor approximation. We then derive an efficient method to compute the exact SkewGP posterior and use it as surrogate model for PBO employing standard acquisition functions (Upper Credible Bound, etc.). We illustrate the benefits of our exact PBO-SkewGP in a variety of experiments, by showing that it consistently outperforms PBO based on Laplace's approximation both in terms of convergence speed and computational time. We also show that our framework can be extended to deal with mixed preferential-categorical BO, where binary judgments (valid or non-valid) together with preference judgments are available.