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This paper addresses the problem of distributed task offloading centred at individual user terminals in a cellular multi-access edge computing (MEC) system. We introduce an online learning-assisted algorithm based on distributed bandit optimization (DBO) to cope with time-varying cost and time-varying constraint functions with unknown statistics on-the-go. The proposed algorithm jointly exploits the projected dual gradient iterations and a greedy method as well as a single broadcast communicating the MEC states to the users at the end of each decision cycle to minimize task computing-communication delay in the long run at user terminals. To track the performance of the proposed online learning algorithm over time, we define a dynamic regret to assess the closeness of the underlying delay cost of the DBO to a clairvoyant dynamic optimum, and an aggregate violation metric to evaluate the asymptotic satisfaction of the constraints. We derive lower and upper bounds for dynamic regret as well as an upper-bound for the aggregate violation and show that the upper-bounds are sub-linear under sub-linear accumulated hindsight variations. The simulation results and comparisons confirm the effectiveness of the proposed algorithm in the long run.
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