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We consider the problem of designing and training a neural network-based orchestrator for fog computing service deployment. Our goal is to train an orchestrator able to optimize diversified and competing QoS requirements, such as blocking probability and service delay, while potentially supporting thousands of fog nodes. To cope with said challenges, we implement our neural orchestrator as a Deep Set (DS) network operating on sets of fog nodes, and we leverage Deep Reinforcement Learning (DRL) with invalid action masking to find an optimal trade-off between competing objectives. Illustrative numerical results show that our Deep Set-based policy generalizes well to problem sizes (i.e., in terms of numbers of fog nodes) up to two orders of magnitude larger than the ones seen during the training phase, outperforming both greedy heuristics and traditional Multi-Layer Perceptron (MLP)-based DRL. In addition …