  We propose an efficient transfer Bayesian optimization method, which finds
the maximum of an expensive-to-evaluate black-box function by using data on
related optimization tasks. Our method uses auxiliary information that
represents the task characteristics to effectively transfer knowledge for
estimating a distribution over target functions. In particular, we use a
Gaussian process, in which the mean and covariance functions are modeled with
neural networks that simultaneously take both the auxiliary information and
feature vectors as input. With a neural network mean function, we can estimate
the target function even without evaluations. By using the neural network
covariance function, we can extract nonlinear correlation among feature vectors
that are shared across related tasks. Our Gaussian process-based formulation
not only enables an analytic calculation of the posterior distribution but also
swiftly adapts the target function to observations. Our method is also
advantageous because the computational costs scale linearly with the number of
source tasks. Through experiments using a synthetic dataset and datasets for
finding the optimal pedestrian traffic regulations and optimal machine learning
algorithms, we demonstrate that our method identifies the optimal points with
fewer target function evaluations than existing methods.
