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Given a new dataset D and a low compute budget, how should we choose a pre-trained model to fine-tune to D, and set the fine-tuning hyperparameters without risking overfitting, particularly if D is small? Here, we extend automated machine learning (AutoML) to best make these choices. Our domain-independent meta-learning approach learns a zero-shot surrogate model which, at test time, allows to select the right deep learning (DL) pipeline (including the pre-trained model and fine-tuning hyperparameters) for a new dataset D given only trivial meta-features describing D such as image resolution or the number of classes. To train this zero-shot model, we collect performance data for many DL pipelines on a large collection of datasets and meta-train on this data to minimize a pairwise ranking objective. We evaluate our approach under the strict time limit of the vision track of the ChaLearn AutoDL challenge benchmark, clearly outperforming all challenge contenders.