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Machine Learning (ML) systems are getting increasingly popular, and drive more and more applications and services in our daily life. This has led to growing concerns over user privacy, since human interaction data typically needs to be transmitted to the cloud in order to train and improve such systems. Federated learning (FL) has recently emerged as a method for training ML models on edge devices using sensitive user data and is seen as a way to mitigate concerns over data privacy. However, since ML models are most commonly trained with label supervision, we need a way to extract labels on edge to make FL viable. In this work, we propose a strategy for training FL models using positive and negative user feedback. We also design a novel framework to study different noise patterns in user feedback, and explore how well standard noise-robust objectives can help mitigate this noise when training models in a federated setting. We evaluate our proposed training setup through detailed experiments on two text classification datasets and analyze the effects of varying levels of user reliability and feedback noise on model performance. We show that our method improves substantially over a self-training baseline, achieving performance closer to models trained with full supervision.