Title: Collaborative Filtering With A Synthetic Feedback Loop. Abstract: We propose a novel learning framework for recommendation systems, assisting collaborative filtering with a synthetic feedback loop. The proposed framework consists of a ``recommender'' and a ``virtual user.'' The recommender is formulizd as a collaborative-filtering method, recommending items according to observed user behavior.  The virtual user estimates rewards from the recommended items and generates the influence of the rewards on observed user behavior.  The recommender connected with the virtual user constructs a closed loop, that recommends users with items and imitates the unobserved feedback of the users to the recommended items. The synthetic feedback is used to augment observed user behavior and improve recommendation results.  Such a model can be interpreted as the inverse reinforcement learning, which can be learned effectively via rollout (simulation). Experimental results show that the proposed framework is able to boost the performance of existing collaborative filtering methods on multiple datasets. 