Privacy-Preserving Distributed Learning with Secret Gradient Descent

In many important application domains of machine learning, data is a privacy-sensitive resource. In addition, due to the growing complexity of the models, single actors typically do not have sufficient data to train a model on their own. Motivated by these challenges, we propose Secret Gradient Descent (SecGD), a method for training machine learning models on data that is spread over different clients while preserving the privacy of the training data. We achieve this by letting each client add temporary noise to the information they send to the server during the training process. They also share this noise in separate messages with the server, which can then subtract it from the previously received values. By routing all data through an anonymization network such as Tor, we prevent the server from knowing which messages originate from the same client, which in turn allows us to show that breaking a client's privacy is computationally intractable as it would require solving a hard instance of the subset sum problem. This setup allows SecGD to work in the presence of only two honest clients and a malicious server, and without the need for peer-to-peer connections.