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The high time needed to reconfigure cloud resources in Network Function Virtualization network environments has led to the proposal of solutions in which a prediction based-resource allocation is performed. All of them are based on traffic or needed resource prediction with the minimization of symmetric loss functions like Mean Squared Error. When inevitable prediction errors are made, the prediction methodologies are not able to differently weigh positive and negative prediction errors that could impact the total network cost. In fact if the predicted traffic is higher than the real one then an over allocation cost, referred to as over-provisioning cost, will be paid by the network operator; conversely, in the opposite case, Quality of Service degradation cost, referred to as under-provisioning cost, will be due to compensate the users because of the resource under allocation. In this paper we propose and investigate a resource allocation strategy based on a Long Short Term Memory algorithm in which the training operation is based on the minimization of an asymmetric cost function that differently weighs the positive and negative prediction errors and the corresponding over-provisioning and under-provisioning costs. In a typical traffic and network scenario, the proposed solution allows for a cost saving by 30% with respect to the case of solution with symmetric cost function.