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We study privacy in a distributed learning framework, where clientscollaboratively build a learning model iteratively through interactions with aserver from whom we need privacy. Motivated by stochastic optimization and thefederated learning (FL) paradigm, we focus on the case where a small fractionof data samples are randomly sub-sampled in each round to participate in thelearning process, which also enables privacy amplification. To obtain evenstronger 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) ofthe clients' responses without their association to each client. The principalresult of this paper is a privacy-optimization performance trade-off fordiscrete randomization mechanisms in this sub-sampled shuffle privacy model.This is enabled through a new theoretical technique to analyze the RenyiDifferential Privacy (RDP) of the sub-sampled shuffle model. We numericallydemonstrate that, for important regimes, with composition our bound yieldssignificant improvement in privacy guarantee over the state-of-the-artapproximate Differential Privacy (DP) guarantee (with strong composition) forsub-sampled shuffled models. We also demonstrate numerically significantimprovement in privacy-learning performance operating point using real datasets.

Renyi Differential Privacy of the Subsampled Shuffle Model in Distributed Learning