Renyi Differential Privacy of the Subsampled Shuffle Model in Distributed Learning

Abstract

We study privacy in a distributed learning framework, where clients collaboratively build a learning model iteratively through interactions 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 their association 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 enabled through a new theoretical technique to analyze the Renyi Differential Privacy (RDP) of the sub-sampled shuffle model. We numerically demonstrate that, for important regimes, with composition our bound yields significant improvement in privacy guarantee over the state-of-the-art approximate Differential Privacy (DP) guarantee (with strong composition) for sub-sampled shuffled models. We also demonstrate numerically significant improvement in privacy-learning performance operating point using real data sets.

arXiv commentarXiv admin note: text overlap with arXiv:2105.05180

References in corpus (12)

• Deep Learning with Differential Privacy
• Federated Learning: Strategies for Improving Communication Efficiency
• Renyi Differential Privacy
• Stochastic Gradient Descent for Non-smooth Optimization: Convergence Results and Optimal Averaging Schemes
• Protection Against Reconstruction and Its Applications in Private Federated Learning
• Subsampled Rényi Differential Privacy and Analytical Moments Accountant
• Rényi Differential Privacy of the Sampled Gaussian Mechanism
• Scalable and Differentially Private Distributed Aggregation in the Shuffled Model
• Encode, Shuffle, Analyze Privacy Revisited: Formalizations and Empirical Evaluation
• Tempered Sigmoid Activations for Deep Learning with Differential Privacy
• Differentially Private Summation with Multi-Message Shuffling
• Improved Summation from Shuffling