  When data are scarce meta-learning can improve a learner's accuracy by
harnessing previous experience from related learning tasks. However, existing
methods have unreliable uncertainty estimates which are often overconfident.
Addressing these shortcomings, we introduce a novel meta-learning framework,
called F-PACOH, that treats meta-learned priors as stochastic processes and
performs meta-level regularization directly in the function space. This allows
us to directly steer the probabilistic predictions of the meta-learner towards
high epistemic uncertainty in regions of insufficient meta-training data and,
thus, obtain well-calibrated uncertainty estimates. Finally, we showcase how
our approach can be integrated with sequential decision making, where reliable
uncertainty quantification is imperative. In our benchmark study on
meta-learning for Bayesian Optimization (BO), F-PACOH significantly outperforms
all other meta-learners and standard baselines.
