  In this paper, the minimization of the weighted sum average age of
information (AoI) in a multi-source status update communication system is
studied. Multiple independent sources send update packets to a common
destination node in a time-slotted manner under the limit of maximum
retransmission rounds. Different multiple access schemes, i.e., orthogonal
multiple access (OMA) and non-orthogonal multiple access (NOMA) are exploited
here over a block-fading multiple access channel (MAC). Constrained Markov
decision process (CMDP) problems are formulated to describe the AoI
minimization problems considering both transmission schemes. The Lagrangian
method is utilised to convert CMDP problems to unconstraint Markov decision
process (MDP) problems and corresponding algorithms to derive the power
allocation policies are obtained. On the other hand, for the case of unknown
environments, two online reinforcement learning approaches considering both
multiple access schemes are proposed to achieve near-optimal age performance.
Numerical simulations validate the improvement of the proposed policy in terms
of weighted sum AoI compared to the fixed power transmission policy, and
illustrate that NOMA is more favorable in case of larger packet size.
