We propose a practical approach based on federated learning to solve out-of-domain issues with continuously running embedded speech-based models such as wake word detectors. We conduct an extensive empirical study of the federated averaging algorithm for the "Hey Snips" wake word based on a crowdsourced dataset that mimics a federation of wake word users. We empirically demonstrate that using an adaptive averaging strategy inspired from Adam in place of standard weighted model averaging highly reduces the number of communication rounds required to reach our target performance. The associated upstream communication costs per user are estimated at 8 MB, which is a reasonable in the context of smart home voice assistants. Additionally, the dataset used for these experiments is being open sourced with the aim of fostering further transparent research in the application of federated learning to speech data.