Ordinal Bayesian Optimisation
This addresses a limitation in Bayesian optimization for practitioners dealing with non-stationary functions, though it appears incremental as it builds on existing methods with a new twist.
The authors tackled the problem of Bayesian optimization failing on ill-conditioned or discontinuous objectives by proposing a new framework that uses only ordering information to fit a Gaussian process in a latent space, demonstrating its capability on challenging toy problems.
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.