Title: Automatic prior selection for meta Bayesian optimization with a case study on tuning deep neural network optimizers. Abstract: The performance of deep neural networks can be highly sensitive to the choice of a variety of meta-parameters, such as optimizer parameters and model hyperparameters. Tuning these well, however, often requires extensive and costly experimentation. Bayesian optimization (BO) is a principled approach to solve such expensive hyperparameter tuning problems efficiently. Key to the performance of BO is specifying and refining a distribution over functions, which is used to reason about the optima of the underlying function being optimized. In this work, we consider the scenario where we have data from similar functions that allows us to specify a tighter distribution a priori. Specifically, we focus on the common but potentially costly task of tuning optimizer parameters for training neural networks. Building on the meta BO method from Wang et al. (2018), we develop practical improvements that (a) boost its performance by leveraging tuning results on multiple tasks without requiring observations for the same meta-parameter points across all tasks, and (b) retain its regret bound for a special case of our method. As a result, we provide a coherent BO solution for iterative optimization of continuous optimizer parameters. To verify our approach in realistic model training setups, we collected a large multi-task hyperparameter tuning dataset by training tens of thousands of configurations of near-state-of-the-art models on popular image and text datasets, as well as a protein sequence dataset. Our results show that on average, our method is able to locate good hyperparameters at least 3 times more efficiently than the best competing methods.