  Transfer learning for Bayesian optimisation has generally assumed a strong
similarity between optimisation tasks, with at least a subset having similar
optimal inputs. This assumption can reduce computational costs, but it is
violated in a wide range of optimisation problems where transfer learning may
nonetheless be useful. We replace this assumption with a weaker one only
requiring the shape of the optimisation landscape to be similar, and analyse
the recent method Prior Learning for Bayesian Optimisation - PLeBO - in this
setting. By learning priors for the hyperparameters of the Gaussian process
surrogate model we can better approximate the underlying function, especially
for few function evaluations. We validate the learned priors and compare to a
breadth of transfer learning approaches, using synthetic data and a recent air
pollution optimisation problem as benchmarks. We show that PLeBO and prior
transfer find good inputs in fewer evaluations.
