Title: On the Power of Pre-training for Generalization in RL: Provable Benefits and Hardness. Abstract: Generalization in Reinforcement Learning (RL) aims to train an agent during training that generalizes to the target environment. In this work, we first point out that RL generalization is fundamentally different from the generalization in supervised learning, and fine-tuning on the target environment is necessary for good test performance. Therefore, we seek to answer the following question: how much can we expect pre-training over training environments to be helpful for efficient and effective fine-tuning? On one hand, we give a surprising result showing that asymptotically, the improvement from pre-training is at most a constant factor. On the other hand, we show that pre-training can be indeed helpful in the non-asymptotic regime by designing a policy collection-elimination (PCE) algorithm and proving a distribution-dependent regret bound that is independent of the state-action space. We hope our theoretical results can provide insight towards understanding pre-training and generalization in RL.