Privacy Amplification by Iteration

Feldman, Vitaly; Mironov, Ilya; Talwar, Kunal; Thakurta, Abhradeep

doi:10.1109/focs.2018.00056

Cited by 97 publications

(178 citation statements)

References 26 publications

(21 reference statements)

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“…Privacy amplification plays a major role in the design of differentially private mechanisms. These include amplification by subsampling [22] and by iteration [16], and the recent seminal work on amplification via shuffling by Erlingsson et al [14]. In particular, Erlingsson et al considered a setting more general than ours which allows for interactive protocols in the shuffle model by first generating a random permutation of the users' inputs and then sequentially applying a (possibly different) local randomizer to each element in the permuted vector.…”

Section: Privacy Amplification By Shufflingmentioning

confidence: 99%

The Privacy Blanket of the Shuffle Model

Balle

Bell

Gascón

et al. 2019

Lecture Notes in Computer Science

168

227

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This work studies differential privacy in the context of the recently proposed shuffle model. Unlike in the local model, where the server collecting privatized data from users can track back an input to a specific user, in the shuffle model users submit their privatized inputs to a server anonymously. This setup yields a trust model which sits in between the classical curator and local models for differential privacy. The shuffle model is the core idea in the Encode, Shuffle, Analyze (ESA) model introduced by Bittau et al. (SOPS 2017). Recent work by Cheu et al. (EUROCRYPT 2019) analyzes the differential privacy properties of the shuffle model and shows that in some cases shuffled protocols provide strictly better accuracy than local protocols. Additionally, Erlingsson et al. (SODA 2019) provide a privacy amplification bound quantifying the level of curator differential privacy achieved by the shuffle model in terms of the local differential privacy of the randomizer used by each user.In this context, we make three contributions. First, we provide an optimal single message protocol for summation of real numbers in the shuffle model. Our protocol is very simple and has better accuracy and communication than the protocols for this same problem proposed by Cheu et al. Optimality of this protocol follows from our second contribution, a new lower bound for the accuracy of private protocols for summation of real numbers in the shuffle model. The third contribution is a new amplification bound for analyzing the privacy of protocols in the shuffle model in terms of the privacy provided by the corresponding local randomizer. Our amplification bound generalizes the results by Erlingsson et al. to a wider range of parameters, and provides a whole family of methods to analyze privacy amplification in the shuffle model. * The Alan Turing Institute. jbell@posteo.net.

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Section: Privacy Amplification By Shufflingmentioning

confidence: 99%

The Privacy Blanket of the Shuffle Model

Balle

Bell

Gascón

et al. 2019

Lecture Notes in Computer Science

168

227

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“…We start by describing a general version of noisy SGD and analyze its privacy using the privacy amplification by iteration technique from [15]. Recall that in our problem we are given a family of convex loss functions over some convex set K ⊆ R parameterized by ∈ X, that is ( , ) is convex and differentiable in the first parameter for every ∈ X.…”

Section: Dp Sco Via Privacy Amplification By Iterationmentioning

confidence: 99%

“…The analysis of this algorithm relies on two tools. The first one is privacy amplification by iteration [15]. This privacy amplification technique ensures that for the purposes of analyzing the privacy guarantees of a point used at step one can effectively treat all the noise added at subsequent steps as also added to the gradient of the loss at .…”

Section: Introductionmentioning

confidence: 99%

“…This privacy amplification technique ensures that for the purposes of analyzing the privacy guarantees of a point used at step one can effectively treat all the noise added at subsequent steps as also added to the gradient of the loss at . A direct application of this technique to noisy SGD results in different privacy guarantees for different points [15] and, as a result, the points used in the last ( ) steps will not have sufficient privacy guarantees. However, we show that by increasing the batch size in those steps we can achieve the optimal privacy guarantees for all the points.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Private stochastic convex optimization: optimal rates in linear time

Feldman

Koren

Talwar

2020

Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

Self Cite

169

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We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019) has established the optimal bound on the excess population loss achievable given samples. Unfortunately, their algorithm achieving this bound is relatively inefficient: it requires (min{ 3/2 , 5/2 / }) gradient computations, where is the dimension of the optimization problem. We describe two new techniques for deriving DP convex optimization algorithms both achieving the optimal bound on excess loss and using (min{ , 2 / }) gradient computations. In particular, the algorithms match the running time of the optimal nonprivate algorithms. The first approach relies on the use of variable batch sizes and is analyzed using the privacy amplification by iteration technique of Feldman et al. (2018). The second approach is based on a general reduction to the problem of localizing an approximately optimal solution with differential privacy. Such localization, in turn, can be achieved using existing (non-private) uniformly stable optimization algorithms. As in the earlier work, our algorithms require a mild smoothness assumption. We also give a linear-time optimal algorithm for the strongly convex case, as well as a faster algorithm for the non-smooth case. CCS CONCEPTS • Theory of computation → Mathematical optimization; Machine learning theory; • Security and privacy → Privacypreserving protocols.

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“…Parametrizing the privacy oracle P δ in terms of a fixed δ stems from the convention that ε is considered the most important privacy parameter 3 , whereas δ is chosen to be a negligibly small value (δ 1/n). This choice is also aligned with recent uses of DP in machine learning where the privacy analysis is conducted under the framework of Rényi DP [39] and the reported privacy is obtained a posteriori by converting the guarantees to standard (ε, δ)-DP for some fixed δ [1,18,22,38,48]. In particular, in our experiments with gradient perturbation for stochastic optimization methods (Sec.…”

Section: Remark 1 (Privacy Oracle)mentioning

confidence: 99%

Automatic Discovery of Privacy–Utility Pareto Fronts

Avent

González

Diethe

et al. 2020

Proceedings on Privacy Enhancing Technologies

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Differential privacy is a mathematical framework for privacy-preserving data analysis. Changing the hyperparameters of a differentially private algorithm allows one to trade off privacy and utility in a principled way. Quantifying this trade-off in advance is essential to decision-makers tasked with deciding how much privacy can be provided in a particular application while maintaining acceptable utility. Analytical utility guarantees offer a rigorous tool to reason about this tradeoff, but are generally only available for relatively simple problems. For more complex tasks, such as training neural networks under differential privacy, the utility achieved by a given algorithm can only be measured empirically. This paper presents a Bayesian optimization methodology for efficiently characterizing the privacy– utility trade-off of any differentially private algorithm using only empirical measurements of its utility. The versatility of our method is illustrated on a number of machine learning tasks involving multiple models, optimizers, and datasets.

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Privacy Amplification by Iteration

Cited by 97 publications

References 26 publications

The Privacy Blanket of the Shuffle Model

The Privacy Blanket of the Shuffle Model

Private stochastic convex optimization: optimal rates in linear time

Automatic Discovery of Privacy–Utility Pareto Fronts

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