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Generalization in Reinforcement Learning (RL) aims to learn an agent duringtraining that generalizes to the target environment. This paper studies RLgeneralization from a theoretical aspect: how much can we expect pre-trainingover training environments to be helpful? When the interaction with the targetenvironment is not allowed, we certify that the best we can obtain is anear-optimal policy in an average sense, and we design an algorithm thatachieves this goal. Furthermore, when the agent is allowed to interact with thetarget environment, we give a surprising result showing that asymptotically,the improvement from pre-training is at most a constant factor. On the otherhand, in the non-asymptotic regime, we design an efficient algorithm and provea distribution-based regret bound in the target environment that is independentof the state-action space.

On the Power of Pre-training for Generalization in RL: Provable Benefits and Hardness