In this paper we prove that the sample complexity of properly learning a class of Littlestone dimension $d$ with approximate differential privacy is $\tilde O(d^6)$, ignoring privacy and accuracy parameters. This result answers a question of Bun et al. (FOCS 2020) by improving upon their upper bound of $2^{O(d)}$ on the sample complexity. Prior to our work, finiteness of the sample complexity for privately learning a class of finite Littlestone dimension was only known for improper private learners, and the fact that our learner is proper answers another question of Bun et al., which was also asked by Bousquet et al. (NeurIPS 2020). Using machinery developed by Bousquet et al., we then show that the sample complexity of sanitizing a binary hypothesis class is at most polynomial in its Littlestone dimension and dual Littlestone dimension. This implies that a class is sanitizable if and only if it has finite Littlestone dimension. An important ingredient of our proofs is a new property of binary hypothesis classes that we call irreducibility, which may be of independent interest.
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 Cambridge（剑桥大学）；Element AI；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization bounds on data-dependent posteriors. Using this flexibility, however, is difficult, especially when the data distribution is presumed to be unknown. We show how an ε-differentially private data-dependent prior yields a valid PAC-Bayes bound, and then show how non-private mechanisms for choosing priors can also yield generalization bounds. As an application of t…
In this paper, we address the problem of privacy-preserving training and evaluation of neural networks in an $N$-party, federated learning setting. We propose a novel system, POSEIDON, the first of its kind in the regime of privacy-preserving neural network training. It employs multiparty lattice-based cryptography to preserve the confidentiality of the training data, the model, and the evaluation data, under a passive-adversary model and collusions between up to $N-1$ parties. To efficiently execute the secure backpropagation algorithm for training neural networks, we provide a generic packin…
IBM Research - Almaden（IBM阿尔马登研究中心）；LIAFA, Université Paris 7（巴黎第七大学LIAFA实验室）；CNRS（法国国家科学研究中心）；Université Paris 7（巴黎第七大学）；Harvard’s Center for Research on Computation and Society (CRCS)（哈佛大学计算与社会研究中心）
In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by Dwork et al. (2006) that ensures that the output of an algorithm leaks little information about the data point provided by any of the participating individuals. Sample complexity of private PAC and agnostic learning was studied in a number of prior works starting with (Kasiviswanathan et al., 2008) but a number of basic questions still remain open, most notably whether learning with privacy requires more samples …
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…
Identifying anomaly multimedia traffic in cyberspace is a big challenge in distributed service systems, multiple generation networks and future internet of everything. This letter explores meta-generalization for a multiparty privacy learning model in graynet to improve the performance of anomaly multimedia traffic identification. The multiparty privacy learning model in graynet is a globally shared model that is partitioned, distributed and trained by exchanging multiparty parameters updates with preserving private data. The meta-generalization refers to discovering the inherent attributes of…
We investigate the direct-sum problem in the context of differentially private PAC learning: What is the sample complexity of solving $k$ learning tasks simultaneously under differential privacy, and how does this cost compare to that of solving $k$ learning tasks without privacy? In our setting, an individual example consists of a domain element $x$ labeled by $k$ unknown concepts $(c_1,\ldots,c_k)$. The goal of a multi-learner is to output $k$ hypotheses $(h_1,\ldots,h_k)$ that generalize the input examples. Without concern for privacy, the sample complexity needed to simultaneously learn $k…
Georgia Institute of Technology（佐治亚理工学院）；Carnegie Mellon University（卡内基梅隆大学）；IBM Research（IBM研究院）；Tel Aviv University（特拉维夫大学）
We consider the problem of PAC-learning from distributed data and analyze fundamental communication complexity questions involved. We provide general upper and lower bounds on the amount of communication needed to learn well, showing that in addition to VC-dimension and covering number, quantities such as the teaching-dimension and mistake-bound of a class play an important role. We also present tight results for a number of common concept classes including conjunctions, parity functions, and decision lists. For linear separators, we show that for non-concentrated distributions, we can use a v…
California Institute of Technology（加州理工学院）；Hebrew University of Jerusalem（希伯来大学）；Ben-Gurion University（本-古里安大学）；Harvard University（哈佛大学）；University of Pennsylvania（宾夕法尼亚大学）
The traditional notion of generalization---i.e., learning a hypothesis whose empirical error is close to its true error---is surprisingly brittle. As has recently been noted in [DFH+15b], even if several algorithms have this guarantee in isolation, the guarantee need not hold if the algorithms are composed adaptively. In this paper, we study three notions of generalization---increasing in strength---that are robust to postprocessing and amenable to adaptive composition, and examine the relationships between them. We call the weakest such notion Robust Generalization. A second, intermediate, no…
University of Minnesota（明尼苏达大学）；DeepMind；Microsoft Research（微软研究院）；Carnegie Mellon University（卡内基梅隆大学）
Motivated by high-stakes decision-making domains like personalized medicine where user information is inherently sensitive, we design privacy preserving exploration policies for episodic reinforcement learning (RL). We first provide a meaningful privacy formulation using the notion of joint differential privacy (JDP)--a strong variant of differential privacy for settings where each user receives their own sets of output (e.g., policy recommendations). We then develop a private optimism-based learning algorithm that simultaneously achieves strong PAC and regret bounds, and enjoys a JDP guarante…
Purdue University（普渡大学）；University of Waterloo（滑铁卢大学）
Online learning has become increasingly popular on handling massive data. The sequential nature of online learning, however, requires a centralized learner to store data and update parameters. In this paper, we consider online learning with {\em distributed} data sources. The autonomous learners update local parameters based on local data sources and periodically exchange information with a small subset of neighbors in a communication network. We derive the regret bound for strongly convex functions that generalizes the work by Ram et al. (2010) for convex functions. Most importantly, we show …
Ensuring differential privacy of models learned from sensitive user data is an important goal that has been studied extensively in recent years. It is now known that for some basic learning problems, especially those involving high-dimensional data, producing an accurate private model requires much more data than learning without privacy. At the same time, in many applications it is not necessary to expose the model itself. Instead users may be allowed to query the prediction model on their inputs only through an appropriate interface. Here we formulate the problem of ensuring privacy of indiv…
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…
University of Toronto（多伦多大学）；Columbia University（哥伦比亚大学）
We study two basic statistical tasks in non-interactive local differential privacy (LDP): learning and refutation. Learning requires finding a concept that best fits an unknown target function (from labelled samples drawn from a distribution), whereas refutation requires distinguishing between data distributions that are well-correlated with some concept in the class, versus distributions where the labels are random. Our main result is a complete characterization of the sample complexity of agnostic PAC learning for non-interactive LDP protocols. We show that the optimal sample complexity for …
UBTECH Sydney AI Centre, School of Computer Science, Faculty of Engineering, the University of Sydney（悉尼大学工程学院计算机科学学院优必选悉尼人工智能中心）；University of Science and Technology of China（中国科学技术大学）
This paper studies the relationship between generalization and privacy preservation in iterative learning algorithms by two sequential steps. We first establish an alignment between generalization and privacy preservation for any learning algorithm. We prove that $(\varepsilon, δ)$-differential privacy implies an on-average generalization bound for multi-database learning algorithms which further leads to a high-probability bound for any learning algorithm. This high-probability bound also implies a PAC-learnable guarantee for differentially private learning algorithms. We then investigate how…
The privacy implications of generative adversarial networks (GANs) are a topic of great interest, leading to several recent algorithms for training GANs with privacy guarantees. By drawing connections to the generalization properties of GANs, we prove that under some assumptions, GAN-generated samples inherently satisfy some (weak) privacy guarantees. First, we show that if a GAN is trained on m samples and used to generate n samples, the generated samples are (epsilon, delta)-differentially-private for (epsilon, delta) pairs where delta scales as O(n/m). We show that under some special condit…
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…
Soochow University（苏州大学）；University of Tsukuba（筑波大学）
Median regression analysis has robustness properties which make it attractive compared with regression based on the mean, while differential privacy can protect individual privacy during statistical analysis of certain datasets. In this paper, three privacy preserving methods are proposed for median regression. The first algorithm is based on a finite smoothing method, the second provides an iterative way and the last one further employs the greedy coordinate descent approach. Privacy preserving properties of these three methods are all proved. Accuracy bound or convergence properties of these…
