In this work, we study the trade-off between differential privacy and adversarial robustness under L2-perturbations in the context of learning halfspaces. We prove nearly tight bounds on the sample complexity of robust private learning of halfspaces for a large regime of parameters. A highlight of our results is that robust and private learning is harder than robust or private learning alone. We complement our theoretical analysis with experimental results on the MNIST and USPS datasets, for a learning algorithm that is both differentially private and adversarially robust.
We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex optimization, the sample complexity of our algorithms depends only on the margin of the data, and not on the dimension. We complement our results with a lower bound, showing that the dependence of our upper bounds on the margin is optimal.
Tel Aviv University（特拉维夫大学）；Google Research（谷歌研究院）；Ben-Gurion University（本-古里安大学）
We present a differentially private learner for halfspaces over a finite grid $G$ in $\mathbb{R}^d$ with sample complexity $\approx d^{2.5}\cdot 2^{\log^*|G|}$, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a $d^2$ factor. The building block for our learner is a new differentially private algorithm for approximately solving the linear feasibility problem: Given a feasible collection of $m$ linear constraints of the form $Ax\geq b$, the task is to privately identify a solution $x$ that satisfies most of the constraints. Our algorithm is iterative, where each iterat…
We present a private learner for halfspaces over an arbitrary finite domain $X\subset \mathbb{R}^d$ with sample complexity $mathrm{poly}(d,2^{\log^*|X|})$. The building block for this learner is a differentially private algorithm for locating an approximate center point of $m>\mathrm{poly}(d,2^{\log^*|X|})$ points -- a high dimensional generalization of the median function. Our construction establishes a relationship between these two problems that is reminiscent of the relation between the median and learning one-dimensional thresholds [Bun et al.\ FOCS '15]. This relationship suggests that t…
Boston University（波士顿大学）；Simon Fraser University（西蒙弗雷泽大学）；University of California, San Diego（加利福尼亚大学圣地亚哥分校）
We introduce a simple framework for designing private boosting algorithms. We give natural conditions under which these algorithms are differentially private, efficient, and noise-tolerant PAC learners. To demonstrate our framework, we use it to construct noise-tolerant and private PAC learners for large-margin halfspaces whose sample complexity does not depend on the dimension. We give two sample complexity bounds for our large-margin halfspace learner. One bound is based only on differential privacy, and uses this guarantee as an asset for ensuring generalization. This first bound illustrate…
We analyze the properties of adversarial training for learning adversarially robust halfspaces in the presence of agnostic label noise. Denoting $\mathsf{OPT}_{p,r}$ as the best robust classification error achieved by a halfspace that is robust to perturbations of $\ell_{p}$ balls of radius $r$, we show that adversarial training on the standard binary cross-entropy loss yields adversarially robust halfspaces up to (robust) classification error $\tilde O(\sqrt{\mathsf{OPT}_{2,r}})$ for $p=2$, and $\tilde O(d^{1/4} \sqrt{\mathsf{OPT}_{\infty, r}} + d^{1/2} \mathsf{OPT}_{\infty,r})$ when $p=\inft…
Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；State University of New York at Buffalo（纽约州立大学布法罗分校）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
In this paper, we study the problem of PAC learning halfspaces in the non-interactive local differential privacy model (NLDP). To breach the barrier of exponential sample complexity, previous results studied a relaxed setting where the server has access to some additional public but unlabeled data. We continue in this direction. Specifically, we consider the problem under the standard setting instead of the large margin setting studied before. Under different mild assumptions on the underlying data distribution, we propose two approaches that are based on the Massart noise model and self-super…
University of Pennsylvania（宾夕法尼亚大学）；University of Minnesota（明尼苏达大学）
We develop theory for using heuristics to solve computationally hard problems in differential privacy. Heuristic approaches have enjoyed tremendous success in machine learning, for which performance can be empirically evaluated. However, privacy guarantees cannot be evaluated empirically, and must be proven --- without making heuristic assumptions. We show that learning problems over broad classes of functions can be solved privately and efficiently, assuming the existence of a non-private oracle for solving the same problem. Our first algorithm yields a privacy guarantee that is contingent on…
Constructing a differentially private (DP) estimator requires deriving the maximum influence of an observation, which can be difficult in the absence of exogenous bounds on the input data or the estimator, especially in high dimensional settings. This paper shows that standard notions of statistical depth, i.e., halfspace depth and regression depth, are particularly advantageous in this regard, both in the sense that the maximum influence of a single observation is easy to analyze and that this value is typically low. This is used to motivate new approximate DP location and regression estimato…
The halfspace depth is a prominent tool of nonparametric multivariate analysis. The upper level sets of the depth, termed the trimmed regions of a measure, serve as a natural generalization of the quantiles and inter-quantile regions to higher-dimensional spaces. The smallest non-empty trimmed region, coined the halfspace median of a measure, generalizes the median. We focus on the (inverse) ray basis theorem for the halfspace depth, a crucial theoretical result that characterizes the halfspace median by a covering property. First, a novel elementary proof of that statement is provided, under …
University of Southern California（南加州大学）；University of California, San Diego（加州大学圣地亚哥分校）
We study the efficient learnability of geometric concept classes - specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces - when a fraction of the data is adversarially corrupted. We give the first polynomial-time PAC learning algorithms for these concept classes with dimension-independent error guarantees in the presence of nasty noise under the Gaussian distribution. In the nasty noise model, an omniscient adversary can arbitrarily corrupt a small fraction of both the unlabeled data points and their labels. This model generalizes well-studied noise mod…
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 Southern California（南加利福尼亚大学）；Amazon Alexa（亚马逊 Alexa）
Deep Neural Networks, despite their great success in diverse domains, are provably sensitive to small perturbations on correctly classified examples and lead to erroneous predictions. Recently, it was proposed that this behavior can be combatted by optimizing the worst case loss function over all possible substitutions of training examples. However, this can be prone to weighing unlikely substitutions higher, limiting the accuracy gain. In this paper, we study adversarial robustness through randomized perturbations, which has two immediate advantages: (1) by ensuring that substitution likeliho…
Toyota Technological Institute at Chicago（芝加哥丰田技术研究院）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
We study the problem of learning adversarially robust halfspaces in the distribution-independent setting. In the realizable setting, we provide necessary and sufficient conditions on the adversarial perturbation sets under which halfspaces are efficiently robustly learnable. In the presence of random label noise, we give a simple computationally efficient algorithm for this problem with respect to any $\ell_p$-perturbation.
Harvard University（哈佛大学）；Northeastern University（东北大学）；Google New York（谷歌纽约）；University of Pennsylvania（宾夕法尼亚大学）
In the \emph{shuffle model} of differential privacy, data-holding users send randomized messages to a secure shuffler, the shuffler permutes the messages, and the resulting collection of messages must be differentially private with regard to user data. In the \emph{pan-private} model, an algorithm processes a stream of data while maintaining an internal state that is differentially private with regard to the stream data. We give evidence connecting these two apparently different models. Our results focus on \emph{robustly} shuffle private protocols, whose privacy guarantees are not greatly aff…
We give the first polynomial time and sample $(ε, δ)$-differentially private (DP) algorithm to estimate the mean, covariance and higher moments in the presence of a constant fraction of adversarial outliers. Our algorithm succeeds for families of distributions that satisfy two well-studied properties in prior works on robust estimation: certifiable subgaussianity of directional moments and certifiable hypercontractivity of degree 2 polynomials. Our recovery guarantees hold in the "right affine-invariant norms": Mahalanobis distance for mean, multiplicative spectral and relative Frobenius dista…
We establish a simple connection between robust and differentially-private algorithms: private mechanisms which perform well with very high probability are automatically robust in the sense that they retain accuracy even if a constant fraction of the samples they receive are adversarially corrupted. Since optimal mechanisms typically achieve these high success probabilities, our results imply that optimal private mechanisms for many basic statistics problems are robust. We investigate the consequences of this observation for both algorithms and computational complexity across different statist…
LINE Corporation（LINE公司）；University of Tsukuba（筑波大学）
We study locally differentially private algorithms for reinforcement learning to obtain a robust policy that performs well across distributed private environments. Our algorithm protects the information of local agents' models from being exploited by adversarial reverse engineering. Since a local policy is strongly being affected by the individual environment, the output of the agent may release the private information unconsciously. In our proposed algorithm, local agents update the model in their environments and report noisy gradients designed to satisfy local differential privacy (LDP) tha…
University of Technology Sydney（悉尼科技大学）；National University of Singapore（新加坡国立大学）；City University of Hong Kong（香港城市大学）；Global Business College of Australia（澳大利亚全球商学院）
It is challenging for stochastic optimizations to handle large-scale sensitive data safely. Recently, Duchi et al. proposed private sampling strategy to solve privacy leakage in stochastic optimizations. However, this strategy leads to robustness degeneration, since this strategy is equal to the noise injection on each gradient, which adversely affects updates of the primal variable. To address this challenge, we introduce a robust stochastic optimization under the framework of local privacy, which is called Privacy-pREserving StochasTIc Gradual lEarning (PRESTIGE). PRESTIGE bridges private up…
University of Washington（华盛顿大学）；Google Research（谷歌研究院）
We study the canonical statistical estimation problem of linear regression from $n$ i.i.d.~examples under $(\varepsilon,δ)$-differential privacy when some response variables are adversarially corrupted. We propose a variant of the popular differentially private stochastic gradient descent (DP-SGD) algorithm with two innovations: a full-batch gradient descent to improve sample complexity and a novel adaptive clipping to guarantee robustness. When there is no adversarial corruption, this algorithm improves upon the existing state-of-the-art approach and achieves a near optimal sample complexity.…
We develop theoretically guaranteed stochastic methods for outlier-robust PCA. Outlier-robust PCA seeks an underlying low-dimensional linear subspace from a dataset that is corrupted with outliers. We are able to show that our methods, which involve stochastic geodesic gradient descent over the Grassmannian manifold, converge and recover an underlying subspace in various regimes through the development of a novel convergence analysis. The main application of this method is an effective differentially private algorithm for outlier-robust PCA that uses a Gaussian noise mechanism within the stoch…
In this work, we study high-dimensional mean estimation under user-level differential privacy, and design an $(\varepsilon,δ)$-differentially private mechanism using as few users as possible. In particular, we provide a nearly optimal trade-off between the number of users and the number of samples per user required for private mean estimation, even when the number of users is as low as $O(\frac{1}{\varepsilon}\log\frac{1}δ)$. Interestingly, this bound on the number of \emph{users} is independent of the dimension (though the number of \emph{samples per user} is allowed to depend polynomially on…
National University of Singapore（新加坡国立大学）；Monash University（莫纳什大学）；The University of Melbourne（墨尔本大学）
It has been demonstrated that hidden representation learned by a deep model can encode private information of the input, hence can be exploited to recover such information with reasonable accuracy. To address this issue, we propose a novel approach called Differentially Private Neural Representation (DPNR) to preserve the privacy of the extracted representation from text. DPNR utilises Differential Privacy (DP) to provide a formal privacy guarantee. Further, we show that masking words via dropout can further enhance privacy. To maintain utility of the learned representation, we integrate DP-no…
We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local differential privacy noise. The ambiguity set is shown to contain the probability distribution of unperturbed, clean data. The radius of the ambiguity set is a function of the privacy budget, spread of the data, and the size of the problem. Hence, machine learning with locally-differentially private datasets can be rewritten as a distributionally-robust optimizat…
In statistical learning and analysis from shared data, which is increasingly widely adopted in platforms such as federated learning and meta-learning, there are two major concerns: privacy and robustness. Each participating individual should be able to contribute without the fear of leaking one's sensitive information. At the same time, the system should be robust in the presence of malicious participants inserting corrupted data. Recent algorithmic advances in learning from shared data focus on either one of these threats, leaving the system vulnerable to the other. We bridge this gap for the…
Adversarial training was introduced as a way to improve the robustness of deep learning models to adversarial attacks. This training method improves robustness against adversarial attacks, but increases the models vulnerability to privacy attacks. In this work we demonstrate how model inversion attacks, extracting training data directly from the model, previously thought to be intractable become feasible when attacking a robustly trained model. The input space for a traditionally trained model is dominated by adversarial examples - data points that strongly activate a certain class but lack se…
University of Wisconsin, Madison（威斯康星大学麦迪逊分校）；University of California, San Diego（加利福尼亚大学圣迭戈分校）；Google Research, Mountain View（谷歌研究院（山景城））
We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $L_p$ perturbations. We give a computationally efficient learning algorithm and a nearly matching computational hardness result for this problem. An interesting implication of our findings is that the $L_{\infty}$ perturbations case is provably computationally harder than the case $2 \leq p < \infty$.
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）；University of Helsinki（赫尔辛基大学）
We propose an algorithm for the adaptation of the learning rate for stochastic gradient descent (SGD) that avoids the need for validation set use. The idea for the adaptiveness comes from the technique of extrapolation: to get an estimate for the error against the gradient flow which underlies SGD, we compare the result obtained by one full step and two half-steps. The algorithm is applied in two separate frameworks: federated and differentially private learning. Using examples of deep neural networks we empirically show that the adaptive algorithm is competitive with manually tuned commonly u…
Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper learning rules fall far from answering the need. In this work we study the fundamental paradigm of (robust) $\textit{empirical risk minimization}$ (RERM), a simple process in which the learner outputs any hypothesis minimizing its training error. RERM famously fails to robustly learn VC classes (Montasser et al., 2019a), a bound we show extends even to `nice' set…
University of California, San Diego（加利福尼亚大学圣迭戈分校）；Microsoft Research（微软研究院）
Differential privacy is a cryptographically-motivated definition of privacy which has gained significant attention over the past few years. Differentially private solutions enforce privacy by adding random noise to a function computed over the data, and the challenge in designing such algorithms is to control the added noise in order to optimize the privacy-accuracy-sample size tradeoff. This work studies differentially-private statistical estimation, and shows upper and lower bounds on the convergence rates of differentially private approximations to statistical estimators. Our results reveal…
With increasing usage of deep learning algorithms in many application, new research questions related to privacy and adversarial attacks are emerging. However, the deep learning algorithm improvement needs more and more data to be shared within research community. Methodologies like federated learning, differential privacy, additive secret sharing provides a way to train machine learning models on edge without moving the data from the edge. However, it is very computationally intensive and prone to adversarial attacks. Therefore, this work introduces a privacy preserving FedCollabNN framework …
University of Wisconsin, Madison（威斯康星大学麦迪逊分校）；University of California, San Diego（加利福尼亚大学圣地亚哥分校）；University of California, Berkeley（加利福尼亚大学伯克利分校）；Google Research（谷歌研究院）
We study the problem of {\em properly} learning large margin halfspaces in the agnostic PAC model. In more detail, we study the complexity of properly learning $d$-dimensional halfspaces on the unit ball within misclassification error $α\cdot \mathrm{OPT}_γ + ε$, where $\mathrm{OPT}_γ$ is the optimal $γ$-margin error rate and $α\geq 1$ is the approximation ratio. We give learning algorithms and computational hardness results for this problem, for all values of the approximation ratio $α\geq 1$, that are nearly-matching for a range of parameters. Specifically, for the natural setting that $α$ i…
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…
McMaster University（麦克马斯特大学）；Vector Institute（向量研究院）；Google（谷歌）；University of Toronto（多伦多大学）
We present a fairly general framework for reducing $(\varepsilon, δ)$ differentially private (DP) statistical estimation to its non-private counterpart. As the main application of this framework, we give a polynomial time and $(\varepsilon,δ)$-DP algorithm for learning (unrestricted) Gaussian distributions in $\mathbb{R}^d$. The sample complexity of our approach for learning the Gaussian up to total variation distance $α$ is $\widetilde{O}(d^2/α^2 + d^2\sqrt{\ln(1/δ)}/α\varepsilon + d\ln(1/δ) / α\varepsilon)$ matching (up to logarithmic factors) the best known information-theoretic (non-effici…
OpenMined；Manifold Computing Group（曼尼福德计算集团）；Ford R&A（福特研发部门）；Harvard University（哈佛大学）；Indian Institute of Technology Jodhpur（印度理工学院焦特布尔分校）；University of Oxford（牛津大学）
In this paper we measure the effectiveness of $ε$-Differential Privacy (DP) when applied to medical imaging. We compare two robust differential privacy mechanisms: Local-DP and DP-SGD and benchmark their performance when analyzing medical imagery records. We analyze the trade-off between the model's accuracy and the level of privacy it guarantees, and also take a closer look to evaluate how useful these theoretical privacy guarantees actually prove to be in the real world medical setting.
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Wayne State University（韦恩州立大学）；Shandong University（山东大学）
We study private and robust multi-armed bandits (MABs), where the agent receives Huber's contaminated heavy-tailed rewards and meanwhile needs to ensure differential privacy. We first present its minimax lower bound, characterizing the information-theoretic limit of regret with respect to privacy budget, contamination level and heavy-tailedness. Then, we propose a meta-algorithm that builds on a private and robust mean estimation sub-routine \texttt{PRM} that essentially relies on reward truncation and the Laplace mechanism only. For two different heavy-tailed settings, we give specific scheme…
Khoury College of Computer Science, Northeastern University（东北大学库利计算机学院）；Apple（苹果公司）
We study the relationship between two desiderata of algorithms in statistical inference and machine learning: differential privacy and robustness to adversarial data corruptions. Their conceptual similarity was first observed by Dwork and Lei (STOC 2009), who observed that private algorithms satisfy robustness, and gave a general method for converting robust algorithms to private ones. However, all general methods for transforming robust algorithms into private ones lead to suboptimal error rates. Our work gives the first black-box transformation that converts any adversarially robust algorith…
Technical University of Munich（慕尼黑工业大学）；Imperial College London（伦敦帝国学院）；Helmholtz Zentrum München（慕尼黑亥姆霍兹中心）
In federated learning for medical image analysis, the safety of the learning protocol is paramount. Such settings can often be compromised by adversaries that target either the private data used by the federation or the integrity of the model itself. This requires the medical imaging community to develop mechanisms to train collaborative models that are private and robust against adversarial data. In response to these challenges, we propose a practical open-source framework to study the effectiveness of combining differential privacy, model compression and adversarial training to improve the r…
