  We consider a scenario where multiple users, powered by energy harvesting,
send version updates over a fading multiple access channel (MAC) to an access
point (AP). Version updates having random importance weights arrive at a user
according to an exogenous arrival process, and a new version renders all
previous versions obsolete. As energy harvesting imposes a time-varying peak
power constraint, it is not possible to deliver all the bits of a version
instantaneously. Accordingly, the AP chooses the objective of minimizing a
finite-horizon time average expectation of the product of importance weight and
a convex increasing function of the number of remaining bits of a version to be
transmitted at each time instant. The objective enables importance-aware
delivery of as many bits, as soon as possible. In this setup, the AP optimizes
the objective function subject to an achievable rate-region constraint of the
MAC and energy constraints at the users, by deciding the transmit power and the
number of bits to be transmitted by each user. We obtain a Markov Decision
Process (MDP)-based optimal online policy to the problem and derive structural
properties of the policy. We then develop a neural network (NN)-based online
heuristic policy, for which we train an NN on the optimal offline policy
derived for different sample paths of energy, version arrival and channel power
gain processes. Via numerical simulations, we observe that the NN-based online
policy performs competitively with respect to the MDP-based online policy.
