  Two of the main principles underlying the life cycle of an artificial
intelligence (AI) module in communication networks are adaptation and
monitoring. Adaptation refers to the need to adjust the operation of an AI
module depending on the current conditions; while monitoring requires measures
of the reliability of an AI module's decisions. Classical frequentist learning
methods for the design of AI modules fall short on both counts of adaptation
and monitoring, catering to one-off training and providing overconfident
decisions. This paper proposes a solution to address both challenges by
integrating meta-learning with Bayesian learning. As a specific use case, the
problems of demodulation and equalization over a fading channel based on the
availability of few pilots are studied. Meta-learning processes pilot
information from multiple frames in order to extract useful shared properties
of effective demodulators across frames. The resulting trained demodulators are
demonstrated, via experiments, to offer better calibrated soft decisions, at
the computational cost of running an ensemble of networks at run time. The
capacity to quantify uncertainty in the model parameter space is further
leveraged by extending Bayesian meta-learning to an active setting. In it, the
designer can select in a sequential fashion channel conditions under which to
generate data for meta-learning from a channel simulator. Bayesian active
meta-learning is seen in experiments to significantly reduce the number of
frames required to obtain efficient adaptation procedure for new frames.
