Title: Off-Dynamics Reinforcement Learning: Training for Transfer with Domain Classifiers. Abstract: We propose a simple, practical, and intuitive approach for domain adaptation in reinforcement learning. Our approach stems from the idea that the agent's experience in the source domain should look similar to its experience in the target domain. Building off of a probabilistic view of RL, we achieve this goal by compensating for the difference in dynamics by modifying the reward function. This modified reward function is simple to estimate by learning auxiliary classifiers that distinguish source-domain transitions from target-domain transitions. Intuitively, the agent is penalized for transitions that would indicate that the agent is interacting with the source domain, rather than the target domain. Formally, we prove that applying our method in the source domain is guaranteed to obtain a near-optimal policy for the target domain, provided that the source and target domains satisfy a lightweight assumption. Our approach is applicable to domains with continuous states and actions and does not require learning an explicit model of the dynamics. On discrete and continuous control tasks, we illustrate the mechanics of our approach and demonstrate its scalability to high-dimensional~tasks.