  This work studies a real-time environment monitoring scenario in the
Industrial Internet of Things (IIoT), where wireless sensors proactively
collect environmental data and transmit it to the controller. We adopt the
notion of risk-sensitivity in financial mathematics as the objective to jointly
minimize the mean, variance, and other higher-order statistics of the network
energy consumption subject to the constraints on the AoI threshold violation
probability and the AoI exceedances over a pre-defined threshold. We
characterize the extreme AoI staleness using results in extreme value theory
and propose a distributed power allocation approach by weaving in together
principles of Lyapunov optimization and federated learning (FL). Simulation
results demonstrate that the proposed FL-based distributed solution is on par
with the centralized baseline while consuming 28.50% less system energy and
outperforms the other baselines.
