Title: When is Offline Hyperparameter Selection Feasible for Reinforcement Learning?. Abstract: Hyperparameter selection is a critical procedure before deploying reinforcement learning algorithms in real-world applications. However, hyperparameter selection prior to deployment requires selecting policies offline without online execution, which is a significant challenge known as offline policy selection. As yet, there is little understanding about the fundamental limitations of the offline policy selection problem. To contribute to our understanding of this problem, in this paper, we investigate when sample efficient offline policy selection is possible. As off-policy policy evaluation (OPE) is a natural approach for policy selection, the sample complexity of offline policy selection is therefore upper-bounded by the number of samples needed to perform OPE. In addition, we prove that the sample complexity of offline policy selection is also lower-bounded by the sample complexity of OPE. These results imply not only that offline policy selection is effective when OPE is effective, but also that sample efficient policy selection is not possible without additional assumptions that make OPE effective. Moreover, we theoretically study the conditions under which offline policy selection using Fitted Q evaluation (FQE) and the Bellman error is sample efficient. We conclude with an empirical study comparing FQE and Bellman errors for offline policy selection.