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The interaction of conversational systems with users poses an exciting opportunity for improving them after deployment, but little evidence has been provided of its feasibility. In most applications, users are not able to provide the correct answer to the system, but they are able to provide binary (correct, incorrect) feedback. In this paper we propose feedback-weighted learning based on importance sampling to improve upon an initial supervised system using binary user feedback. We perform simulated experiments on document classification (for development) and Conversational Question Answering datasets like QuAC and DoQA, where binary user feedback is derived from gold annotations. The results show that our method is able to improve over the initial supervised system, getting close to a fully-supervised system that has access to the same labeled examples in in-domain experiments (QuAC), and even matching in out-of-domain experiments (DoQA). Our work opens the prospect to exploit interactions with real users and improve conversational systems after deployment.