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The Poisson Binomial Mechanism for Unbiased Federated Learning with Secure Aggregation
Wei-Ning Chen · Ayfer Ozgur · Peter Kairouz

Wed Jul 20 03:30 PM -- 05:30 PM (PDT) @ Hall E #1021
We introduce the Poisson Binomial mechanism (PBM), a discrete differential privacy mechanism for distributed mean estimation (DME) with applications to federated learning and analytics. We provide a tight analysis of its privacy guarantees, showing that it achieves the same privacy-accuracy trade-offs as the continuous Gaussian mechanism. Our analysis is based on a novel bound on the R\'enyi divergence of two Poisson binomial distributions that may be of independent interest. Unlike previous discrete DP schemes based on additive noise, our mechanism encodes local information into a parameter of the binomial distribution, and hence the output distribution is discrete with bounded support. Moreover, the support does not increase as the privacy budget goes to zero as in the case of additive schemes which require the addition of more noise to achieve higher privacy; on the contrary, the support becomes smaller as eps goes to zero. The bounded support enables us to combine our mechanism with secure aggregation (SecAgg), a multi-party cryptographic protocol, without the need of performing modular clipping which results in an unbiased estimator of the sum of the local vectors. This in turn allows us to apply it in the private FL setting and provide an upper bound on the convergence rate of the SGD algorithm. Moreover, since the support of the output distribution becomes smaller as $\varepsilon \ra 0$, the communication cost of our scheme decreases with the privacy constraint $\varepsilon$, outperforming all previous distributed DP schemes based on additive noise in the high privacy or low communication regimes.

Author Information

Wei-Ning Chen (Stanford University)
Wei-Ning Chen

Wei-Ning Chen is currently a Ph.D. student at Stanford EE under the support of Stanford Graduate Fellowship (SGF). His research interests broadly lie in information-theoretic and algorithmic aspects of data science. He adopt tools mainly from information theory, theoretical machine learning, and statistical inference, with a current focus on distributed inference, federated learning and differential privacy.

Ayfer Ozgur (Stanford University)
Peter Kairouz (Google)

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