Ordinal Bayesian Optimisation

TL;DR

This paper introduces a novel Bayesian optimisation framework that relies solely on variable orderings, making it robust to non-stationary and discontinuous objective functions, and demonstrates its effectiveness on challenging problems.

Contribution

It proposes a new ordering-based Bayesian optimisation method that is agnostic to original metrics and provides algorithms with proven regret bounds.

Findings

Effective on ill-conditioned and discontinuous problems

Outperforms traditional methods in challenging scenarios

Provides theoretical regret guarantees

Abstract

Bayesian optimisation is a powerful tool to solve expensive black-box problems, but fails when the stationary assumption made on the objective function is strongly violated, which is the case in particular for ill-conditioned or discontinuous objectives. We tackle this problem by proposing a new Bayesian optimisation framework that only considers the ordering of variables, both in the input and output spaces, to fit a Gaussian process in a latent space. By doing so, our approach is agnostic to the original metrics on the original spaces. We propose two algorithms, respectively based on an optimistic strategy and on Thompson sampling. For the optimistic strategy we prove an optimal performance under the measure of regret in the latent space. We illustrate the capability of our framework on several challenging toy problems.