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Exploiting the computational heterogeneity of mobile devices and edge nodes, mobile edge computation (MEC) provides an efficient approach to achieving real-time applications that are sensitive to information freshness, by offloading tasks from mobile devices to edge nodes. We use the metric Age-of-Information (AoI) to evaluate information freshness. An efficient solution to minimize the AoI for the MEC system with multiple users is non-trivial to obtain due to the random computing time. In this paper, we consider multiple users offloading tasks to heterogeneous edge servers in a MEC system. We first reformulate the problem as a Restless Multi-Arm-Bandit (RMAB) problem and establish a hierarchical Markov Decision Process (MDP) to characterize the updating of AoI for the MEC system. Based on the hierarchical MDP, we propose a nested index framework and design a nested index policy with provably …