  The efficient exchange of information is an essential aspect of intelligent
collective behavior. Event-triggered control and estimation achieve some
efficiency by replacing continuous data exchange between agents with
intermittent, or event-triggered communication. Typically, model-based
predictions are used at times of no data transmission, and updates are sent
only when the prediction error grows too large. The effectiveness in reducing
communication thus strongly depends on the quality of the prediction model. In
this article, we propose event-triggered learning as a novel concept to reduce
communication even further and to also adapt to changing dynamics. By
monitoring the actual communication rate and comparing it to the one that is
induced by the model, we detect a mismatch between model and reality and
trigger model learning when needed. Specifically, for linear Gaussian dynamics,
we derive different classes of learning triggers solely based on a statistical
analysis of inter-communication times and formally prove their effectiveness
with the aid of concentration inequalities.
