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Offline reinforcement learning (RL purely from logged data) is an important avenue for deploying RL techniques in real-world scenarios. However, existing hyperparameter selection methods for offline RL break the offline assumption by evaluating policies corresponding to each hyperparameter setting in the environment. This online execution is often infeasible and hence undermines the main aim of offline RL. Therefore, in this work, we focus on \textit{offline hyperparameter selection}, i.e. methods for choosing the best policy from a set of many policies trained using different hyperparameters, given only logged data. Through large-scale empirical evaluation we show that: 1) offline RL algorithms are not robust to hyperparameter choices, 2) factors such as the offline RL algorithm and method for estimating Q values can have a big impact on hyperparameter selection, and 3) when we control those factors carefully, we can reliably rank policies across hyperparameter choices, and therefore choose policies which are close to the best policy in the set. Overall, our results present an optimistic view that offline hyperparameter selection is within reach, even in challenging tasks with pixel observations, high dimensional action spaces, and long horizon.