In this paper, we study efficient differentially private alternating direction methods of multipliers (ADMM) via gradient perturbation for many machine learning problems. For smooth convex loss functions with (non)-smooth regularization, we propose the first differentially private ADMM (DP-ADMM) algorithm with performance guarantee of $(ε,δ)$-differential privacy ($(ε,δ)$-DP). From the viewpoint of theoretical analysis, we use the Gaussian mechanism and the conversion relationship between Rényi Differential Privacy (RDP) and DP to perform a comprehensive privacy analysis for our algorithm. Then we establish a new criterion to prove the convergence of the proposed algorithms including DP-ADMM. We also give the utility analysis of our DP-ADMM. Moreover, we propose an accelerated DP-ADMM (DP-AccADMM) with the Nesterov's acceleration technique. Finally, we conduct numerical experiments on many real-world datasets to show the privacy-utility tradeoff of the two proposed algorithms, and all the comparative analysis shows that DP-AccADMM converges faster and has a better utility than DP-ADMM, when the privacy budget $ε$ is larger than a threshold.
University of Houston（休斯顿大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；University of Science and Technology of China（中国科学技术大学）
Due to massive amounts of data distributed across multiple locations, distributed machine learning has attracted a lot of research interests. Alternating Direction Method of Multipliers (ADMM) is a powerful method of designing distributed machine learning algorithm, whereby each agent computes over local datasets and exchanges computation results with its neighbor agents in an iterative procedure. There exists significant privacy leakage during this iterative process if the local data is sensitive. In this paper, we propose a differentially private ADMM algorithm (P-ADMM) to provide dynamic ze…
Oklahoma State University（俄克拉荷马州立大学）；University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）
Alternating Direction Method of Multipliers (ADMM) is a popular algorithm for distributed learning, where a network of nodes collaboratively solve a regularized empirical risk minimization by iterative local computation associated with distributed data and iterate exchanges. When the training data is sensitive, the exchanged iterates will cause serious privacy concern. In this paper, we aim to propose a new differentially private distributed ADMM algorithm with improved accuracy for a wide range of convex learning problems. In our proposed algorithm, we adopt the approximation of the objective…
University of Houston（休斯顿大学）；San Francisco State University（旧金山州立大学）；University of Connecticut（康涅狄格大学）
The Alternating Direction Method of Multipliers (ADMM) and its distributed version have been widely used in machine learning. In the iterations of ADMM, model updates using local private data and model exchanges among agents impose critical privacy concerns. Despite some pioneering works to relieve such concerns, differentially private ADMM still confronts many research challenges. For example, the guarantee of differential privacy (DP) relies on the premise that the optimality of each local problem can be perfectly attained in each ADMM iteration, which may never happen in practice. The model…
Boston University（波士顿大学）；Centrum Wiskunde & Informatica（荷兰国家数学与计算机科学研究所）；Microsoft Research（微软研究院）
Correlation clustering is a widely used technique in unsupervised machine learning. Motivated by applications where individual privacy is a concern, we initiate the study of differentially private correlation clustering. We propose an algorithm that achieves subquadratic additive error compared to the optimal cost. In contrast, straightforward adaptations of existing non-private algorithms all lead to a trivial quadratic error. Finally, we give a lower bound showing that any pure differentially private algorithm for correlation clustering requires additive error of $Ω(n)$.
In this paper we consider the problem of minimizing composite objective functions consisting of a convex differentiable loss function plus a non-smooth regularization term, such as $L_1$ norm or nuclear norm, under Rényi differential privacy (RDP). To solve the problem, we propose two stochastic alternating direction method of multipliers (ADMM) algorithms: ssADMM based on gradient perturbation and mpADMM based on output perturbation. Both algorithms decompose the original problem into sub-problems that have closed-form solutions. The first algorithm, ssADMM, applies the recent privacy amplifi…
Khoury College of Computer Sciences, Northeastern University（东北大学胡里计算机科学学院）
We study the problem of differentially private constrained maximization of decomposable submodular functions. A submodular function is decomposable if it takes the form of a sum of submodular functions. The special case of maximizing a monotone, decomposable submodular function under cardinality constraints is known as the Combinatorial Public Projects (CPP) problem [Papadimitriou et al., 2008]. Previous work by Gupta et al. [2010] gave a differentially private algorithm for the CPP problem. We extend this work by designing differentially private algorithms for both monotone and non-monotone d…
Machine learning practitioners frequently seek to leverage the most informative available data, without violating the data owner's privacy, when building predictive models. Differentially private data synthesis protects personal details from exposure, and allows for the training of differentially private machine learning models on privately generated datasets. But how can we effectively assess the efficacy of differentially private synthetic data? In this paper, we survey four differentially private generative adversarial networks for data synthesis. We evaluate each of them at scale on five s…
Khoury College of Computer Sciences, Northeastern University（东北大学胡里计算机科学学院）
We investigate whether Differentially Private SGD offers better privacy in practice than what is guaranteed by its state-of-the-art analysis. We do so via novel data poisoning attacks, which we show correspond to realistic privacy attacks. While previous work (Ma et al., arXiv 2019) proposed this connection between differential privacy and data poisoning as a defense against data poisoning, our use as a tool for understanding the privacy of a specific mechanism is new. More generally, our work takes a quantitative, empirical approach to understanding the privacy afforded by specific implementa…
In this note, we describe a simple approach to obtain a differentially private algorithm for k-clustering with nearly the same multiplicative factor as any non-private counterpart at the cost of a large polynomial additive error. The approach is the combination of a simple geometric observation independent of privacy consideration and any existing private algorithm with a constant approximation.
Google Research（谷歌研究院）；Blavatnik School of Computer Science, Tel Aviv University（特拉维夫大学布拉瓦特尼克计算机科学学院）；Ben-Gurion University（本-古里安大学）
Clustering is a fundamental problem in data analysis. In differentially private clustering, the goal is to identify $k$ cluster centers without disclosing information on individual data points. Despite significant research progress, the problem had so far resisted practical solutions. In this work we aim at providing simple implementable differentially private clustering algorithms that provide utility when the data is "easy," e.g., when there exists a significant separation between the clusters. We propose a framework that allows us to apply non-private clustering algorithms to the easy insta…
We revisit the problem of $n$-gram extraction in the differential privacy setting. In this problem, given a corpus of private text data, the goal is to release as many $n$-grams as possible while preserving user level privacy. Extracting $n$-grams is a fundamental subroutine in many NLP applications such as sentence completion, response generation for emails etc. The problem also arises in other applications such as sequence mining, and is a generalization of recently studied differentially private set union (DPSU). In this paper, we develop a new differentially private algorithm for this prob…
We develop a new reduction that converts any online convex optimization algorithm suffering $O(\sqrt{T})$ regret into an $ε$-differentially private stochastic convex optimization algorithm with the optimal convergence rate $\tilde O(1/\sqrt{T} + \sqrt{d}/εT)$ on smooth losses in linear time, forming a direct analogy to the classical non-private "online-to-batch" conversion. By applying our techniques to more advanced adaptive online algorithms, we produce adaptive differentially private counterparts whose convergence rates depend on apriori unknown variances or parameter norms.
Columbia University（哥伦比亚大学）；NTUA（雅典国立技术大学）；Northeastern University（东北大学）
We provide computationally efficient, differentially private algorithms for the classical regression settings of Least Squares Fitting, Binary Regression and Linear Regression with unbounded covariates. Prior to our work, privacy constraints in such regression settings were studied under strong a priori bounds on covariates. We consider the case of Gaussian marginals and extend recent differentially private techniques on mean and covariance estimation (Kamath et al., 2019; Karwa and Vadhan, 2018) to the sub-gaussian regime. We provide a novel technical analysis yielding differentially private …
We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially the same approximation ratios as those that can be obtained by any non-private algorithm, while incurring only small additive errors. This improves upon existing efficient algorithms that only achieve some large constant approximation factors. Our results also imply an improved algorithm for the Sample and Aggregate privacy framework. Furthermore, we show tha…
University of Georgia（佐治亚大学）；The Pennsylvania State University（宾夕法尼亚州立大学）
Standard methods for differentially private training of deep neural networks replace back-propagated mini-batch gradients with biased and noisy approximations to the gradient. These modifications to training often result in a privacy-preserving model that is significantly less accurate than its non-private counterpart. We hypothesize that alternative training algorithms may be more amenable to differential privacy. Specifically, we examine the suitability of direct feedback alignment (DFA). We propose the first differentially private method for training deep neural networks with DFA and show t…
Argonne National Laboratory（阿贡国家实验室）；Mathematics and Computer Science Division（数学与计算机科学部）；Lemont, IL 60439（美国伊利诺伊州莱蒙特市（60439））
Differential privacy (DP) techniques can be applied to the federated learning model to protect data privacy against inference attacks to communication among the learning agents. The DP techniques, however, hinder achieving a greater learning performance while ensuring strong data privacy. In this paper we develop a DP inexact alternating direction method of multipliers algorithm that solves a sequence of subproblems with the objective perturbation by random noises generated from a Laplace distribution. We show that our algorithm provides $\barε$-DP for every iteration, where $\barε$ is a priva…
In this paper, we study the differentially private empirical risk minimization problem where the parameter is constrained to a Riemannian manifold. We introduce a framework of differentially private Riemannian optimization by adding noise to the Riemannian gradient on the tangent space. The noise follows a Gaussian distribution intrinsically defined with respect to the Riemannian metric. We adapt the Gaussian mechanism from the Euclidean space to the tangent space compatible to such generalized Gaussian distribution. We show that this strategy presents a simple analysis as compared to directly…
This paper presents a differentially private algorithm for linear regression learning in a decentralized fashion. Under this algorithm, privacy budget is theoretically derived, in addition to that the solution error is shown to be bounded by $O(t)$ for $O(1/t)$ descent step size and $O(\exp(t^{1-e}))$ for $O(t^{-e})$ descent step size.
Northwest University（西北大学）；Macau University of Science and Technology（澳门科技大学）
In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers (ADMM) algorithm. The theoretical results and empirical results that show the utility of the proposed methods are also provided.
We demonstrate that differentially private machine learning has not yet reached its "AlexNet moment" on many canonical vision tasks: linear models trained on handcrafted features significantly outperform end-to-end deep neural networks for moderate privacy budgets. To exceed the performance of handcrafted features, we show that private learning requires either much more private data, or access to features learned on public data from a similar domain. Our work introduces simple yet strong baselines for differentially private learning that can inform the evaluation of future progress in this are…
We study differentially private mean estimation in a high-dimensional setting. Existing differential privacy techniques applied to large dimensions lead to computationally intractable problems or estimators with excessive privacy loss. Recent work in high-dimensional robust statistics has identified computationally tractable mean estimation algorithms with asymptotic dimension-independent error guarantees. We incorporate these results to develop a strict bound on the global sensitivity of the robust mean estimator. This yields a computationally tractable algorithm for differentially private me…
University of Chicago（芝加哥大学）；Toyota Technological Institute at Chicago（芝加哥丰田工业大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We propose an adaptive (stochastic) gradient perturbation method for differentially private empirical risk minimization. At each iteration, the random noise added to the gradient is optimally adapted to the stepsize; we name this process adaptive differentially private (ADP) learning. Given the same privacy budget, we prove that the ADP method considerably improves the utility guarantee compared to the standard differentially private method in which vanilla random noise is added. Our method is particularly useful for gradient-based algorithms with time-varying learning rates, including variant…
Oklahoma State University（俄克拉荷马州立大学）；The University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；Loyola University Chicago（芝加哥洛约拉大学）
Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems…
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
Differential privacy is a formal, mathematical definition of data privacy that has gained traction in academia, industry, and government. The task of correctly constructing differentially private algorithms is non-trivial, and mistakes have been made in foundational algorithms. Currently, there is no automated support for converting an existing, non-private program into a differentially private version. In this paper, we propose a technique for automatically learning an accurate and differentially private version of a given non-private program. We show how to solve this difficult program synth…
Differentially private models seek to protect the privacy of data the model is trained on, making it an important component of model security and privacy. At the same time, data scientists and machine learning engineers seek to use uncertainty quantification methods to ensure models are as useful and actionable as possible. We explore the tension between uncertainty quantification via dropout and privacy by conducting membership inference attacks against models with and without differential privacy. We find that models with large dropout slightly increases a model's risk to succumbing to membe…
Clustering is an essential primitive in unsupervised machine learning. We bring forth the problem of sublinear-time differentially-private clustering as a natural and well-motivated direction of research. We combine the $k$-means and $k$-median sublinear-time results of Mishra et al. (SODA, 2001) and of Czumaj and Sohler (Rand. Struct. and Algorithms, 2007) with recent results on private clustering of Balcan et al. (ICML 2017), Gupta et al. (SODA, 2010) and Ghazi et al. (NeurIPS, 2020) to obtain sublinear-time private $k$-means and $k$-median algorithms via subsampling. We also investigate the…
Differential privacy (DP) techniques can be applied to the federated learning model to statistically guarantee data privacy against inference attacks to communication among the learning agents. While ensuring strong data privacy, however, the DP techniques hinder achieving a greater learning performance. In this paper we develop a DP inexact alternating direction method of multipliers algorithm with multiple local updates for federated learning, where a sequence of convex subproblems is solved with the objective perturbation by random noises generated from a Laplace distribution. We show that …
Differentially private synthetic data generation offers a recent solution to release analytically useful data while preserving the privacy of individuals in the data. In order to utilize these algorithms for public policy decisions, policymakers need an accurate understanding of these algorithms' comparative performance. Correspondingly, data practitioners require standard metrics for evaluating the analytic qualities of the synthetic data. In this paper, we present an in-depth evaluation of several differentially private synthetic data algorithms using actual differentially private synthetic …
An important use of private data is to build machine learning classifiers. While there is a burgeoning literature on differentially private classification algorithms, we find that they are not practical in real applications due to two reasons. First, existing differentially private classifiers provide poor accuracy on real world datasets. Second, there is no known differentially private algorithm for empirically evaluating the private classifier on a private test dataset. In this paper, we develop differentially private algorithms that mirror real world empirical machine learning workflows. We…
Learning from continuous data streams via classification/regression is prevalent in many domains. Adapting to evolving data characteristics (concept drift) while protecting data owners' private information is an open challenge. We present a differentially private ensemble solution to this problem with two distinguishing features: it allows an \textit{unbounded} number of ensemble updates to deal with the potentially never-ending data streams under a fixed privacy budget, and it is \textit{model agnostic}, in that it treats any pre-trained differentially private classification/regression model …
Columbia University, Department of Statistics（哥伦比亚大学统计系）；ENSAE ParisTech, Department of Statistics（巴黎高等经济商业学院统计系）
We derive concentration inequalities for differentially private median and mean estimators building on the "Propose, Test, Release" (PTR) mechanism introduced by Dwork and Lei (2009). We introduce a new general version of the PTR mechanism that allows us to derive high probability error bounds for differentially private estimators. Our algorithms provide the first statistical guarantees for differentially private estimation of the median and mean without any boundedness assumptions on the data, and without assuming that the target population parameter lies in some known bounded interval. Our p…
The Pennsylvania State University（宾夕法尼亚州立大学）；University of Georgia（佐治亚大学）
The process of data mining with differential privacy produces results that are affected by two types of noise: sampling noise due to data collection and privacy noise that is designed to prevent the reconstruction of sensitive information. In this paper, we consider the problem of designing confidence intervals for the parameters of a variety of differentially private machine learning models. The algorithms can provide confidence intervals that satisfy differential privacy (as well as the more recently proposed concentrated differential privacy) and can be used with existing differentially pri…
Department of Computer Science, Georgetown University（乔治城大学计算机科学系）
We present the first nearly optimal differentially private PAC learner for any concept class with VC dimension 1 and Littlestone dimension $d$. Our algorithm achieves the sample complexity of $\tilde{O}_{\varepsilon,δ,α,δ}(\log^* d)$, nearly matching the lower bound of $Ω(\log^* d)$ proved by Alon et al. [STOC19]. Prior to our work, the best known upper bound is $\tilde{O}(VC\cdot d^5)$ for general VC classes, as shown by Ghazi et al. [STOC21].
The widespread deployment of machine learning (ML) is raising serious concerns on protecting the privacy of users who contributed to the collection of training data. Differential privacy (DP) is rapidly gaining momentum in the industry as a practical standard for privacy protection. Despite DP's importance, however, little has been explored within the computer systems community regarding the implication of this emerging ML algorithm on system designs. In this work, we conduct a detailed workload characterization on a state-of-the-art differentially private ML training algorithm named DP-SGD. W…
This paper studies the problem of clustering in metric spaces while preserving the privacy of individual data. Specifically, we examine differentially private variants of the k-medians and Euclidean k-means problems. We present polynomial algorithms with constant multiplicative error and lower additive error than the previous state-of-the-art for each problem. Additionally, our algorithms use a clustering algorithm without differential privacy as a black-box. This allows practitioners to control the trade-off between runtime and approximation factor by choosing a suitable clustering algorithm …
We present the first differentially private algorithms for reinforcement learning, which apply to the task of evaluating a fixed policy. We establish two approaches for achieving differential privacy, provide a theoretical analysis of the privacy and utility of the two algorithms, and show promising results on simple empirical examples.
University of Alberta（阿尔伯塔大学）；University of Kent（肯特大学）
Distributed machine learning has been widely studied in order to handle exploding amount of data. In this paper, we study an important yet less visited distributed learning problem where features are inherently distributed or vertically partitioned among multiple parties, and sharing of raw data or model parameters among parties is prohibited due to privacy concerns. We propose an ADMM sharing framework to approach risk minimization over distributed features, where each party only needs to share a single value for each sample in the training process, thus minimizing the data leakage risk. We e…
The application of differential privacy to the training of deep neural networks holds the promise of allowing large-scale (decentralized) use of sensitive data while providing rigorous privacy guarantees to the individual. The predominant approach to differentially private training of neural networks is DP-SGD, which relies on norm-based gradient clipping as a method for bounding sensitivity, followed by the addition of appropriately calibrated Gaussian noise. In this work we propose NeuralDP, a technique for privatising activations of some layer within a neural network, which by the post-proc…
College of Information and Computer Sciences（信息与计算机科学学院）；University of Massachusetts（马萨诸塞大学）
Many differentially private algorithms for answering database queries involve a step that reconstructs a discrete data distribution from noisy measurements. This provides consistent query answers and reduces error, but often requires space that grows exponentially with dimension. Private-PGM is a recent approach that uses graphical models to represent the data distribution, with complexity proportional to that of exact marginal inference in a graphical model with structure determined by the co-occurrence of variables in the noisy measurements. Private-PGM is highly scalable for sparse measurem…
University of California San Diego（加州大学圣迭戈分校）；Microsoft Research（微软研究院）；Microsoft（微软）
Recent papers have shown that large pre-trained language models (LLMs) such as BERT, GPT-2 can be fine-tuned on private data to achieve performance comparable to non-private models for many downstream Natural Language Processing (NLP) tasks while simultaneously guaranteeing differential privacy. The inference cost of these models -- which consist of hundreds of millions of parameters -- however, can be prohibitively large. Hence, often in practice, LLMs are compressed before they are deployed in specific applications. In this paper, we initiate the study of differentially private model compres…
In this work, we study local minimax convergence estimation rates subject to $ε$-differential privacy. Unlike worst-case rates, which may be conservative, algorithms that are locally minimax optimal must adapt to easy instances of the problem. We construct locally minimax differentially private estimators for one-parameter exponential families and estimating the tail rate of a distribution. In these cases, we show that optimal algorithms for simple hypothesis testing, namely the recent optimal private testers of Canonne et al. (2019), directly inform the design of locally minimax estimation al…
Linear $L_1$-regularized models have remained one of the simplest and most effective tools in data analysis, especially in information retrieval problems where n-grams over text with TF-IDF or Okapi feature values are a strong and easy baseline. Over the past decade, screening rules have risen in popularity as a way to reduce the runtime for producing the sparse regression weights of $L_1$ models. However, despite the increasing need of privacy-preserving models in information retrieval, to the best of our knoweledge, no differentially private screening rule exists. In this paper, we develop t…
We explore the training of generative adversarial networks with differential privacy to anonymize image data sets. On MNIST, we numerically measure the privacy-utility trade-off using parameters from $ε$-$δ$ differential privacy and the inception score. Our experiments uncover a saturated training regime where an increasing privacy budget adds little to the quality of generated images. We also explain analytically why differentially private Adam optimization is independent of the gradient clipping parameter. Furthermore, we highlight common errors in previous works on differentially private de…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所（HIIT））；Aalto University（阿尔托大学）；University of Helsinki（赫尔辛基大学）
Motivation: Human genomic datasets often contain sensitive information that limits use and sharing of the data. In particular, simple anonymisation strategies fail to provide sufficient level of protection for genomic data, because the data are inherently identifiable. Differentially private machine learning can help by guaranteeing that the published results do not leak too much information about any individual data point. Recent research has reached promising results on differentially private drug sensitivity prediction using gene expression data. Differentially private learning with genomic…
Catastrophic forgetting can be a significant problem for institutions that must delete historic data for privacy reasons. For example, hospitals might not be able to retain patient data permanently. But neural networks trained on recent data alone will tend to forget lessons learned on old data. We present a differentially private continual learning framework based on variational inference. We estimate the likelihood of past data given the current model using differentially private generative models of old datasets.
