Preferential Bayesian optimisation with Skew Gaussian Processes
This work addresses a bottleneck in optimization for scenarios where only preference judgments are available, such as in A/B testing or recommender systems, by providing a more accurate and efficient method, though it is incremental as it builds on existing PBO frameworks.
The paper tackled the problem of approximating the posterior distribution in preferential Bayesian optimization (PBO) by proving that the true posterior is a Skew Gaussian Process (SkewGP) and showing that the commonly used Laplace's method provides a poor approximation. The result is an exact PBO-SkewGP method that consistently outperforms the Laplace-based approach in convergence speed and computational time across various experiments.
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.