  Bayesian optimization (BO) is a widely-used method for optimizing expensive
(to evaluate) problems. At the core of most BO methods is the modeling of the
objective function using a Gaussian Process (GP) whose covariance is selected
from a set of standard covariance functions. From a weight-space view, this
models the objective as a linear function in a feature space implied by the
given covariance K, with an arbitrary Gaussian weight prior ${\bf w} \sim
\mathcal{N} ({\bf 0}, {\bf I})$. In many practical applications there is data
available that has a similar (covariance) structure to the objective, but
which, having different form, cannot be used directly in standard transfer
learning. In this paper we show how such auxiliary data may be used to
construct a GP covariance corresponding to a more appropriate weight prior for
the objective function. Building on this, we show that we may accelerate BO by
modeling the objective function using this (learned) weight prior, which we
demonstrate on both test functions and a practical application to short-polymer
fibre manufacture.
