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

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