Age of Information for Updates with Distortion

We consider an information update system where an information receiver requests updates from an information provider in order to minimize its age of information. The updates are generated at the transmitter as a result of completing a set of tasks such as collecting data and performing computations. We refer to this as the update generation process. We model the $quality$ (i.e., $distortion$) of an update as an increasing (resp. decreasing) function of the processing time spent while generating the update at the transmitter. While processing longer at the transmitter results in a better quality (lower distortion) update, it causes the update to age. We determine the age-optimal policies for the update request times at the receiver and update processing times at the transmitter subject to a minimum required quality (maximum allowed distortion) constraint on the updates.