  Multi-output regression problems are commonly encountered in science and
engineering. In particular, multi-output Gaussian processes have been emerged
as a promising tool for modeling these complex systems since they can exploit
the inherent correlations and provide reliable uncertainty estimates. In many
applications, however, acquiring the data is expensive and safety concerns
might arise (e.g. robotics, engineering). We propose a safe active learning
approach for multi-output Gaussian process regression. This approach queries
the most informative data or output taking the relatedness between the
regressors and safety constraints into account. We prove the effectiveness of
our approach by providing theoretical analysis and by demonstrating empirical
results on simulated datasets and on a real-world engineering dataset. On all
datasets, our approach shows improved convergence compared to its competitors.
