Renyi Differential Privacy of The Subsampled Shuffle Model In Distributed Learning

We study privacy in a distributed learning framework, where clients collaboratively build a learning model iteratively throughinteractions with a server from whom we need privacy. Motivated by stochastic optimization and the federated learning (FL) paradigm, we focus on the case where a small fraction of data samples are randomly sub-sampled in each round to participate in the learning process, which also enables privacy amplification. To obtain even stronger local privacy guarantees, we study this in the shuffle privacy model, where each client randomizes its response using a local differentially private (LDP) mechanism and the server only receives a random permutation (shuffle) of the clients' responses without theirassociation to each client. The principal result of this paper is a privacy-optimization performance trade-off for discrete randomization mechanisms in this sub-sampled shuffle privacy model. This is enabledthrough a new theoretical technique to analyze the Renyi Differential Privacy (RDP) of the sub-sampled shuffle model.