Shuffled Check-in: Privacy Amplification towards Practical Distributed Learning

Recent studies of distributed computation with formal privacy guarantees, such as differentially private (DP) federated learning, leverage random sampling of clients in each round (privacy amplification by subsampling) to achieve satisfactory levels of privacy. Achieving this however requires strong assumptions which may not hold in practice, including precise and uniform subsampling of clients, and a highly trusted aggregator to process clients' data. In this paper, we explore a more practical protocol, shuffled check-in, to resolve the aforementioned issues. The protocol relies on client making independent and random decision to participate in the computation, freeing the requirement of server-initiated subsampling, and enabling robust modelling of client dropouts. Moreover, a weaker trust model known as the shuffle model is employed instead of using a trusted aggregator. To this end, we introduce new tools to characterize the R\'enyi differential privacy (RDP) of shuffled check-in. We show that our new techniques improve at least three times in privacy guarantee over those using approximate DP's strong composition at various parameter regimes. Furthermore, we provide a numerical approach to track the privacy of generic shuffled check-in mechanism including distributed stochastic gradient descent (SGD) with Gaussian mechanism. To the best of our knowledge, this is also the first evaluation of Gaussian mechanism within the local/shuffle model under the distributed setting in the literature, which can be of independent interest.