  The growth in artificial intelligence (AI) technology has attracted
substantial interests in age-of-information (AoI)-aware task offloading of
mobile edge computing (MEC)-namely, minimizing service latency. Additionally,
the use of MEC systems poses an additional problem arising from limited battery
resources of MDs. This paper tackles the pressing challenge of AoI-aware
distributed task offloading optimization, where user association (UA), resource
allocation (RA), full-task offloading, and battery of mobile devices (MDs) are
jointly considered. In existing studies, joint optimization of overall task
offloading and UA is seldom considered due to the complexity of combinatorial
optimization problems, and in cases where it is considered, linear objective
functions such as power consumption are adopted. Revolutionizing the realm of
MEC, our objective includes all major components contributing to users' quality
of experience, including AoI and energy consumption. To achieve this, we first
formulate an NP-hard combinatorial problem, where the objective function
comprises three elements: communication latency, computation latency, and
battery usage. We derive a closed-form RA solution of the problem; next, we
provide a distributed pricing-based UA solution. We simulate the proposed
algorithm for various vision and language AI tasks. Our numerical results show
that the proposed method Pareto-dominates baseline methods. More specifically,
the results demonstrate that the proposed method can outperform baseline
methods by 1.62 times smaller AoI with 41.2% less energy consumption.
