  We study the problem of finding efficient sampling policies in an edge-based
feedback system, where sensor samples are offloaded to a back-end server that
processes them and generates feedback to a user. Sampling the system at maximum
frequency results in the detection of events of interest with minimum delay but
incurs higher energy costs due to the communication and processing of redundant
samples. On the other hand, lower sampling frequency results in higher delay in
detecting the event, thus increasing the idle energy usage and degrading the
quality of experience. We quantify this trade-off as a weighted function
between the number of samples and the sampling interval. We solve the
minimisation problem for exponential and Rayleigh distributions, for the random
time to the event of interest. We prove the convexity of the objective
functions by using novel techniques, which can be of independent interest
elsewhere. We argue that adding an initial offset to the periodic sampling can
further reduce the energy consumption and jointly compute the optimum offset
and sampling interval. We apply our framework to two practically relevant
applications and show energy savings of up to 36% when compared to an existing
periodic scheme.
