Recommending fashion items often leverages rich user profiles and makes targeted suggestions based on past history and previous purchases. In this paper, we work under the assumption that no prior knowledge is given about a user. We propose to build a user profile on the fly by integrating user reactions as we recommend complementary items to compose an outfit. We present a reinforcement learning agent capable of suggesting appropriate garments and ingesting user feedback so to improve its recommendations and maximize user satisfaction. To train such a model, we resort to a proxy model to be able to simulate having user feedback in the training loop. We experiment on the IQON3000 fashion dataset and we find that a reinforcement learning-based agent becomes capable of improving its recommendations by taking into account personal preferences. Furthermore, such task demonstrated to be hard for non-reinforcement models, that cannot exploit exploration during training.