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Behavior cloning (BC) is often practical for robot learning because it allows a policy to be trained offline without rewards, by supervised learning on expert demonstrations. However, BC does not effectively leverage what we will refer to as unlabeled experience: data of mixed and unknown quality without reward annotations. This unlabeled data can be generated by a variety of sources such as human teleoperation, scripted policies and other agents on the same robot. Towards data-driven offline robot learning that can use this unlabeled experience, we introduce Offline Reinforced Imitation Learning (ORIL). ORIL first learns a reward function by contrasting observations from demonstrator and unlabeled trajectories, then annotates all data with the learned reward, and finally trains an agent via offline reinforcement learning. Across a diverse set of continuous control and simulated robotic manipulation tasks, we show that ORIL consistently outperforms comparable BC agents by effectively leveraging unlabeled experience.