Covariance Function Pre-Training with m-Kernels for Accelerated Bayesian Optimisation

TL;DR

This paper introduces a novel covariance function learning method using m-kernels for Bayesian optimisation, enabling automatic problem-specific covariance construction that improves efficiency in experimental design tasks.

Contribution

It proposes a new approach leveraging m-kernels to automatically adapt covariance functions for Bayesian optimisation, reducing manual tuning and enhancing problem-specific modeling.

Findings

Effective on alloy design and polymer manufacturing problems

Outperforms traditional covariance selection methods

Demonstrates faster convergence in Bayesian optimisation

Abstract

The paper presents a novel approach to direct covariance function learning for Bayesian optimisation, with particular emphasis on experimental design problems where an existing corpus of condensed knowledge is present. The method presented borrows techniques from reproducing kernel Banach space theory (specifically m-kernels) and leverages them to convert (or re-weight) existing covariance functions into new, problem-specific covariance functions. The key advantage of this approach is that rather than relying on the user to manually select (with some hyperparameter tuning and experimentation) an appropriate covariance function it constructs the covariance function to specifically match the problem at hand. The technique is demonstrated on two real-world problems - specifically alloy design and short-polymer fibre manufacturing - as well as a selected test function.