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In this paper, we study collaborative filtering (CF) in an interactive setting, in which a recommender system continuously recommends items to individual users and receives interactive feedback. Whilst users enjoy sequential recommendations, the recommendation predictions are constantly refined using up-to-date feedback on the recommended items. Bringing the interactive mechanism back to the CF process is fundamental because the ultimate goal for a recommender system is about the discovery of interesting items for individual users and yet users' personal preferences and contexts evolve over time during the interactions with the system. This requires us not to distinguish between the stages of collecting information to construct the user profile and making recommendations, but to seamlessly integrate these stages together during the interactive process, with the goal of maximizing the overall recommendation accuracy throughout the interactions. This mechanism naturally addresses the cold-start problem as any user can immediately receive sequential recommendations without providing ratings beforehand. We formulate the interactive CF with the probabilistic matrix factorization (PMF) framework, and leverage several exploitation-exploration algorithms to select items, including the empirical Thompson sampling and upper confidence bound based algorithms. We conduct our experiment on cold-start users as well as warm-start users with drifting taste. Results show that the proposed methods have significant improvements over several strong baselines for the MovieLens, EachMovie and Netflix datasets.