Artificial Intelligence (AI) is a key component of 6G networks, as it enables communication and computing services to adapt to end users' requirements and demand patterns. The management of Mobile Edge Computing (MEC) is a meaningful example of AI application: computational resources available at the network edge need to be carefully allocated to users, whose jobs may have different priorities and latency requirements. The research community has developed several AI algorithms to perform this resource allocation, but it has neglected a key aspect: learning is itself a computationally demanding task, and considering free training results in idealized conditions and performance in simulations. In this work, we consider a more realistic case in which the cost of learning is specifically accounted for, presenting a new algorithm to dynamically select when to train a Deep Reinforcement Learning (DRL) agent that allocates resources. Our method is highly general, as it can be directly applied to any scenario involving a training overhead, and it can approach the same performance as an ideal learning agent even under realistic training conditions.