  The age of information metric fails to correctly describe the intrinsic
semantics of a status update. In an intelligent reflecting surface-aided
cooperative relay communication system, we propose the age of semantics (AoS)
for measuring semantics freshness of the status updates. Specifically, we focus
on the status updating from a source node (SN) to the destination, which is
formulated as a Markov decision process (MDP). The objective of the SN is to
maximize the expected satisfaction of AoS and energy consumption under the
maximum transmit power constraint. To seek the optimal control policy, we first
derive an online deep actor-critic (DAC) learning scheme under the on-policy
temporal difference learning framework. However, implementing the online DAC in
practice poses the key challenge in infinitely repeated interactions between
the SN and the system, which can be dangerous particularly during the
exploration. We then put forward a novel offline DAC scheme, which estimates
the optimal control policy from a previously collected dataset without any
further interactions with the system. Numerical experiments verify the
theoretical results and show that our offline DAC scheme significantly
outperforms the online DAC scheme and the most representative baselines in
terms of mean utility, demonstrating strong robustness to dataset quality.
