Distributed Mirror-Prox Optimization for Multi-Access Edge Computing

In this paper, we address the problem of overall delay minimization in a cellular multi-access edge computing (MEC) network, where servers with limited computing and storage resources are co-located with a base station (BS) to execute the computation tasks offloaded by the users. We formulate this problem as a distributed mirror prox (DMP) optimization at individual users and the MEC servers' local controller (LC) over a long-time horizon and develop an online algorithm to ensure queue stability of the overall network in the long run. Both, the cost and the constraint functions are time-varying with unknown statistics. We evaluate the performance of the proposed algorithm using two performance metrics: the dynamic regret to assess the closeness of the achievable cost against the dynamic optimal value; and the aggregate violation to measure the asymptotic satisfaction of the constraints. Given the optimum hindsight variation is sub-linear, we prove that both of the dynamic regret and the aggregate violation are sub-linear in the long run. The simulation results confirm the superiority of the proposed DMP algorithm over the stochastic dual gradient in terms of delay minimization, dynamic regret, aggregate violation and energy efficiency in battery-powered user devices.