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Multi-access edge computing (MEC) has already shown the potential in enabling mobile devices to bear the computation-intensive applications by offloading some tasks to a nearby access point (AP) integrated with a MEC server (MES). However, due to the varying network conditions and limited computation resources of the MES, the offloading decisions taken by a mobile device and the computational resources allocated by the MES may not be efficiently achieved with the lowest cost. In this paper, we propose a dynamic offloading framework for the MEC network, in which the uplink non-orthogonal multiple access (NOMA) is used to enable multiple devices to upload their tasks via the same frequency band. We formulate the offloading decision problem as a multiclass classification problem and formulate the MES computational resource allocation problem as a regression problem. Then a multi-task learning based feedforward neural network (MTFNN) model is designed to jointly optimize the offloading decision and computational resource allocation. Numerical results illustrate that the proposed MTFNN outperforms the conventional optimization method in terms of inference accuracy and computation complexity.