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Added by
Daniel Levy
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We propose and analyze algorithms to solve a range of learning tasks under user-level differential privacy constraints. Rather than guaranteeing only the privacy of individual samples, user-level DP protects a users entire contribution ($m ge 1$ samples), providing more stringent but more realistic protection against information leaks. We show that for high-dimensional mean estimation, empirical risk minimization with smooth losses, stochastic convex optimization, and learning hypothesis class with finite metric entropy, the privacy cost decreases as $O(1/sqrt{m})$ as users provide more samples. In contrast, when increasing the number of users $n$, the privacy cost decreases at a faster $O(1/n)$ rate. We complement these results with lower bounds showing the worst-case optimality of our algorithm for mean estimation and stochastic convex optimization. Our algorithms rely on novel techniques for private mean estimation in arbitrary dimension with error scaling as the concentration radius $tau$ of the distribution rather than the entire range. Under uniform convergence, we derive an algorithm that privately answers a sequence of $K$ adaptively chosen queries with privacy cost proportional to $tau$, and apply it to solve the learning tasks we consider.
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Much of the literature on differential privacy focuses on item-level privacy, where loosely speaking, the goal is to provide privacy per item or training example. However, recently many practical applications such as federated learning require preserving privacy for all items of a single user, which is much harder to achieve. Therefore understanding the theoretical limit of user-level privacy becomes crucial. We study the fundamental problem of learning discrete distributions over $k$ symbols with user-level differential privacy. If each user has $m$ samples, we show that straightforward applications of Laplace or Gaussian mechanisms require the number of users to be $mathcal{O}(k/(malpha^2) + k/epsilonalpha)$ to achieve an $ell_1$ distance of $alpha$ between the true and estimated distributions, with the privacy-induced penalty $k/epsilonalpha$ independent of the number of samples per user $m$. Moreover, we show that any mechanism that only operates on the final aggregate counts should require a user complexity of the same order. We then propose a mechanism such that the number of users scales as $tilde{mathcal{O}}(k/(malpha^2) + k/sqrt{m}epsilonalpha)$ and hence the privacy penalty is $tilde{Theta}(sqrt{m})$ times smaller compared to the standard mechanisms in certain settings of interest. We further show that the proposed mechanism is nearly-optimal under certain regimes. We also propose general techniques for obtaining lower bounds on restricted differentially private estimators and a lower bound on the total variation between binomial distributions, both of which might be of independent interest.
We consider the problem of reinforcing federated learning with formal privacy guarantees. We propose to employ Bayesian differential privacy, a relaxation of differential privacy for similarly distributed data, to provide sharper privacy loss bounds. We adapt the Bayesian privacy accounting method to the federated setting and suggest multiple improvements for more efficient privacy budgeting at different levels. Our experiments show significant advantage over the state-of-the-art differential privacy bounds for federated learning on image classification tasks, including a medical application, bringing the privacy budget below 1 at the client level, and below 0.1 at the instance level. Lower amounts of noise also benefit the model accuracy and reduce the number of communication rounds.
Deep learning models are often trained on datasets that contain sensitive information such as individuals shopping transactions, personal contacts, and medical records. An increasingly important line of work therefore has sought to train neural networks subject to privacy constraints that are specified by differential privacy or its divergence-based relaxations. These privacy definitions, however, have weaknesses in handling certain important primitives (composition and subsampling), thereby giving loose or complicated privacy analyses of training neural networks. In this paper, we consider a recently proposed privacy definition termed textit{$f$-differential privacy} [18] for a refined privacy analysis of training neural networks. Leveraging the appealing properties of $f$-differential privacy in handling composition and subsampling, this paper derives analytically tractable expressions for the privacy guarantees of both stochastic gradient descent and Adam used in training deep neural networks, without the need of developing sophisticated techniques as [3] did. Our results demonstrate that the $f$-differential privacy framework allows for a new privacy analysis that improves on the prior analysis~[3], which in turn suggests tuning certain parameters of neural networks for a better prediction accuracy without violating the privacy budget. These theoretically derived improvements are confirmed by our experiments in a range of tasks in image classification, text classification, and recommender systems. Python code to calculate the privacy cost for these experiments is publicly available in the texttt{TensorFlow Privacy} library.
Traditional differential privacy is independent of the data distribution. However, this is not well-matched with the modern machine learning context, where models are trained on specific data. As a result, achieving meaningful privacy guarantees in ML often excessively reduces accuracy. We propose Bayesian differential privacy (BDP), which takes into account the data distribution to provide more practical privacy guarantees. We also derive a general privacy accounting method under BDP, building upon the well-known moments accountant. Our experiments demonstrate that in-distribution samples in classic machine learning datasets, such as MNIST and CIFAR-10, enjoy significantly stronger privacy guarantees than postulated by DP, while models maintain high classification accuracy.
This paper investigates capabilities of Privacy-Preserving Deep Learning (PPDL) mechanisms against various forms of privacy attacks. First, we propose to quantitatively measure the trade-off between model accuracy and privacy losses incurred by reconstruction, tracing and membership attacks. Second, we formulate reconstruction attacks as solving a noisy system of linear equations, and prove that attacks are guaranteed to be defeated if condition (2) is unfulfilled. Third, based on theoretical analysis, a novel Secret Polarization Network (SPN) is proposed to thwart privacy attacks, which pose serious challenges to existing PPDL methods. Extensive experiments showed that model accuracies are improved on average by 5-20% compared with baseline mechanisms, in regimes where data privacy are satisfactorily protected.
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