arXiv subjects

Badih Ghazi

Publications and source records attributed to Badih Ghazi.

At least 73 records · Page 4Linked to original sources

arXiv2021

Deep Learning with Label Differential Privacy

The Randomized Response (RR) algorithm is a classical technique to improve robustness in survey aggregation, and has been widely adopted in applications with differential privacy guarantees. We propose a novel algorithm, Randomized Response with Prior (RRWithPrior), which can provide more accurate results while maintaining the same level of privacy guaranteed by RR. We then apply RRWithPrior to learn neural networks with label differential privacy (LabelDP), and show that when only the label needs to be protected, the model performance can be significantly improved over the previous state-of-the-art private baselines. Moreover, we study different ways to obtain priors, which when used with RRWithPrior can additionally improve the model performance, further reducing the accuracy gap between private and non-private models. We complement the empirical results with theoretical analysis showing that LabelDP is provably easier than protecting both the inputs and labels.

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arXiv2021

Differentially Private Aggregation in the Shuffle Model: Almost Central Accuracy in Almost a Single Message

The shuffle model of differential privacy has attracted attention in the literature due to it being a middle ground between the well-studied central and local models. In this work, we study the problem of summing (aggregating) real numbers or integers, a basic primitive in numerous machine learning tasks, in the shuffle model. We give a protocol achieving error arbitrarily close to that of the (Discrete) Laplace mechanism in the central model, while each user only sends $1 + o(1)$ short messages in expectation.

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arXiv2021

Large-Scale Differentially Private BERT

In this work, we study the large-scale pretraining of BERT-Large with differentially private SGD (DP-SGD). We show that combined with a careful implementation, scaling up the batch size to millions (i.e., mega-batches) improves the utility of the DP-SGD step for BERT; we also enhance its efficiency by using an increasing batch size schedule. Our implementation builds on the recent work of [SVK20], who demonstrated that the overhead of a DP-SGD step is minimized with effective use of JAX [BFH+18, FJL18] primitives in conjunction with the XLA compiler [XLA17]. Our implementation achieves a masked language model accuracy of 60.5% at a batch size of 2M, for $ε= 5.36$. To put this number in perspective, non-private BERT models achieve an accuracy of $\sim$70%.

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arXiv2021

Google COVID-19 Vaccination Search Insights: Anonymization Process Description

This report describes the aggregation and anonymization process applied to the COVID-19 Vaccination Search Insights (published at http://goo.gle/covid19vaccinationinsights), a publicly available dataset showing aggregated and anonymized trends in Google searches related to COVID-19 vaccination. The applied anonymization techniques protect every user's daily search activity related to COVID-19 vaccinations with $(\varepsilon, δ)$-differential privacy for $\varepsilon = 2.19$ and $δ= 10^{-5}$.

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arXiv2021

Private Counting from Anonymous Messages: Near-Optimal Accuracy with Vanishing Communication Overhead

Differential privacy (DP) is a formal notion for quantifying the privacy loss of algorithms. Algorithms in the central model of DP achieve high accuracy but make the strongest trust assumptions whereas those in the local DP model make the weakest trust assumptions but incur substantial accuracy loss. The shuffled DP model (Bittau et al., 2017; Erlingsson et al., 2019; Cheu et al., 2019) has recently emerged as a feasible middle ground between the central and local models, providing stronger trust assumptions than the former while promising higher accuracies than the latter. In this paper, we obtain practical communication-efficient algorithms in the shuffled DP model for two basic aggregation primitives used in machine learning: 1) binary summation, and 2) histograms over a moderate number of buckets. Our algorithms achieve accuracy that is arbitrarily close to that of central DP algorithms with an expected communication per user essentially matching what is needed without any privacy constraints! We demonstrate the practicality of our algorithms by experimentally comparing their performance to several widely-used protocols such as Randomized Response (Warner, 1965) and RAPPOR (Erlingsson et al., 2014).

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arXiv2021

Locally Private k-Means in One Round

We provide an approximation algorithm for k-means clustering in the one-round (aka non-interactive) local model of differential privacy (DP). This algorithm achieves an approximation ratio arbitrarily close to the best non private approximation algorithm, improving upon previously known algorithms that only guarantee large (constant) approximation ratios. Furthermore, this is the first constant-factor approximation algorithm for k-means that requires only one round of communication in the local DP model, positively resolving an open question of Stemmer (SODA 2020). Our algorithmic framework is quite flexible; we demonstrate this by showing that it also yields a similar near-optimal approximation algorithm in the (one-round) shuffle DP model.

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arXiv2021

Robust and Private Learning of Halfspaces

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.

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arXiv2021

Advances and Open Problems in Federated Learning

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.

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arXiv2020

On Avoiding the Union Bound When Answering Multiple Differentially Private Queries

In this work, we study the problem of answering $k$ queries with $(ε, δ)$-differential privacy, where each query has sensitivity one. We give an algorithm for this task that achieves an expected $\ell_\infty$ error bound of $O(\frac{1}ε\sqrt{k \log \frac{1}δ})$, which is known to be tight (Steinke and Ullman, 2016). A very recent work by Dagan and Kur (2020) provides a similar result, albeit via a completely different approach. One difference between our work and theirs is that our guarantee holds even when $δ< 2^{-Ω(k/(\log k)^8)}$ whereas theirs does not apply in this case. On the other hand, the algorithm of Dagan and Kur has a remarkable advantage that the $\ell_{\infty}$ error bound of $O(\frac{1}ε\sqrt{k \log \frac{1}δ})$ holds not only in expectation but always (i.e., with probability one) while we can only get a high probability (or expected) guarantee on the error.

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arXiv2020

Sample-efficient proper PAC learning with approximate differential privacy

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.

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arXiv2020

Optimality of Correlated Sampling Strategies

In the "correlated sampling" problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to output an element sampled according to their respective distributions, while trying to minimize the probability that their outputs disagree. A well known strategy due to Kleinberg-Tardos and Holenstein, with a close variant (for a similar problem) due to Broder, solves this task with disagreement probability at most $2 δ/(1+δ)$, where $δ$ is the total variation distance between $P$ and $Q$. This strategy has been used in several different contexts, including sketching algorithms, approximation algorithms based on rounding linear programming relaxations, the study of parallel repetition and cryptography. In this paper, we give a surprisingly simple proof that this strategy is essentially optimal. Specifically, for every $δ\in (0,1)$, we show that any correlated sampling strategy incurs a disagreement probability of essentially $2δ/(1+δ)$ on some inputs $P$ and $Q$ with total variation distance at most $δ$. This partially answers a recent question of Rivest. Our proof is based on studying a new problem that we call "constrained agreement". Here, the two players are given subsets $A \subseteq [n]$ and $B \subseteq [n]$, respectively, and their goal is to output an element $i \in A$ and $j \in B$, respectively, while minimizing the probability that $i \neq j$. We prove tight bounds for this question, which in turn imply tight bounds for correlated sampling. Though we settle basic questions about the two problems, our formulation leads to more fine-grained questions that remain open.

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arXiv2020

On Distributed Differential Privacy and Counting Distinct Elements

We study the setup where each of $n$ users holds an element from a discrete set, and the goal is to count the number of distinct elements across all users, under the constraint of $(ε, δ)$-differentially privacy: - In the non-interactive local setting, we prove that the additive error of any protocol is $Ω(n)$ for any constant $ε$ and for any $δ$ inverse polynomial in $n$. - In the single-message shuffle setting, we prove a lower bound of $Ω(n)$ on the error for any constant $ε$ and for some $δ$ inverse quasi-polynomial in $n$. We do so by building on the moment-matching method from the literature on distribution estimation. - In the multi-message shuffle setting, we give a protocol with at most one message per user in expectation and with an error of $\tilde{O}(\sqrt(n))$ for any constant $ε$ and for any $δ$ inverse polynomial in $n$. Our protocol is also robustly shuffle private, and our error of $\sqrt(n)$ matches a known lower bound for such protocols. Our proof technique relies on a new notion, that we call dominated protocols, and which can also be used to obtain the first non-trivial lower bounds against multi-message shuffle protocols for the well-studied problems of selection and learning parity. Our first lower bound for estimating the number of distinct elements provides the first $ω(\sqrt(n))$ separation between global sensitivity and error in local differential privacy, thus answering an open question of Vadhan (2017). We also provide a simple construction that gives $\tildeΩ(n)$ separation between global sensitivity and error in two-party differential privacy, thereby answering an open question of McGregor et al. (2011).

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arXiv2020

Differentially Private Clustering: Tight Approximation Ratios

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 that one of the tools used in our 1-Cluster algorithm can be employed to get a faster quantum algorithm for ClosestPair in a moderate number of dimensions.

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arXiv2020

Near-tight closure bounds for Littlestone and threshold dimensions

We study closure properties for the Littlestone and threshold dimensions of binary hypothesis classes. Given classes $\mathcal{H}_1, \ldots, \mathcal{H}_k$ of Boolean functions with bounded Littlestone (respectively, threshold) dimension, we establish an upper bound on the Littlestone (respectively, threshold) dimension of the class defined by applying an arbitrary binary aggregation rule to $\mathcal{H}_1, \ldots, \mathcal{H}_k$. We also show that our upper bounds are nearly tight. Our upper bounds give an exponential (in $k$) improvement upon analogous bounds shown by Alon et al. (COLT 2020), thus answering a question posed by their work.

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arXiv2020

On the Power of Multiple Anonymous Messages

An exciting new development in differential privacy is the shuffled model, in which an anonymous channel enables non-interactive, differentially private protocols with error much smaller than what is possible in the local model, while relying on weaker trust assumptions than in the central model. In this paper, we study basic counting problems in the shuffled model and establish separations between the error that can be achieved in the single-message shuffled model and in the shuffled model with multiple messages per user. For the problem of frequency estimation for $n$ users and a domain of size $B$, we obtain: - A nearly tight lower bound of $\tildeΩ( \min(\sqrt[4]{n}, \sqrt{B}))$ on the error in the single-message shuffled model. This implies that the protocols obtained from the amplification via shuffling work of Erlingsson et al. (SODA 2019) and Balle et al. (Crypto 2019) are essentially optimal for single-message protocols. A key ingredient in the proof is a lower bound on the error of locally-private frequency estimation in the low-privacy (aka high $ε$) regime. - Protocols in the multi-message shuffled model with $poly(\log{B}, \log{n})$ bits of communication per user and $poly\log{B}$ error, which provide an exponential improvement on the error compared to what is possible with single-message algorithms. For the related selection problem on a domain of size $B$, we prove: - A nearly tight lower bound of $Ω(B)$ on the number of users in the single-message shuffled model. This significantly improves on the $Ω(B^{1/17})$ lower bound obtained by Cheu et al. (Eurocrypt 2019), and when combined with their $\tilde{O}(\sqrt{B})$-error multi-message protocol, implies the first separation between single-message and multi-message protocols for this problem.

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arXiv2020

Pure Differentially Private Summation from Anonymous Messages

The shuffled (aka anonymous) model has recently generated significant interest as a candidate distributed privacy framework with trust assumptions better than the central model but with achievable errors smaller than the local model. We study pure differentially private (DP) protocols in the shuffled model for summation, a basic and widely used primitive: - For binary summation where each of n users holds a bit as an input, we give a pure $ε$-DP protocol for estimating the number of ones held by the users up to an error of $O_ε(1)$, and each user sends $O_ε(\log n)$ messages each of 1 bit. This is the first pure protocol in the shuffled model with error $o(\sqrt{n})$ for constant $ε$. Using this protocol, we give a pure $ε$-DP protocol that performs summation of real numbers in $[0, 1]$ up to an error of $O_ε(1)$, and where each user sends $O_ε(\log^3 n)$ messages each of $O(\log\log n)$ bits. - In contrast, we show that for any pure $ε$-DP protocol for binary summation in the shuffled model having absolute error $n^{0.5-Ω(1)}$, the per user communication has to be at least $Ω_ε(\sqrt{\log n})$ bits. This implies the first separation between the (bounded-communication) multi-message shuffled model and the central model, and the first separation between pure and approximate DP protocols in the shuffled model. To prove our lower bound, we consider (a generalization of) the following question: given $γ$ in $(0, 1)$, what is the smallest m for which there are two random variables $X^0, X^1$ supported on $\{0, \dots ,m\}$ such that (i) the total variation distance between $X^0$ and $X^1$ is at least $1-γ$, and (ii) the moment generating functions of $X^0$ and $X^1$ are within a constant factor of each other everywhere? We show that the answer is $m = Θ(\sqrt{\log(1/γ)})$.

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arXiv2019

Scalable and Differentially Private Distributed Aggregation in the Shuffled Model

Federated learning promises to make machine learning feasible on distributed, private datasets by implementing gradient descent using secure aggregation methods. The idea is to compute a global weight update without revealing the contributions of individual users. Current practical protocols for secure aggregation work in an "honest but curious" setting where a curious adversary observing all communication to and from the server cannot learn any private information assuming the server is honest and follows the protocol. A more scalable and robust primitive for privacy-preserving protocols is shuffling of user data, so as to hide the origin of each data item. Highly scalable and secure protocols for shuffling, so-called mixnets, have been proposed as a primitive for privacy-preserving analytics in the Encode-Shuffle-Analyze framework by Bittau et al., which was later analytically studied by Erlingsson et al. and Cheu et al.. The recent papers by Cheu et al., and Balle et al. have given protocols for secure aggregation that achieve differential privacy guarantees in this "shuffled model". Their protocols come at a cost, though: Either the expected aggregation error or the amount of communication per user scales as a polynomial $n^{Ω(1)}$ in the number of users $n$. In this paper we propose simple and more efficient protocol for aggregation in the shuffled model, where communication as well as error increases only polylogarithmically in $n$. Our new technique is a conceptual "invisibility cloak" that makes users' data almost indistinguishable from random noise while introducing zero distortion on the sum.

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arXiv2019

Private Aggregation from Fewer Anonymous Messages

Consider the setup where $n$ parties are each given a number $x_i \in \mathbb{F}_q$ and the goal is to compute the sum $\sum_i x_i$ in a secure fashion and with as little communication as possible. We study this problem in the anonymized model of Ishai et al. (FOCS 2006) where each party may broadcast anonymous messages on an insecure channel. We present a new analysis of the one-round "split and mix" protocol of Ishai et al. In order to achieve the same security parameter, our analysis reduces the required number of messages by a $Θ(\log n)$ multiplicative factor. We complement our positive result with lower bounds showing that the dependence of the number of messages on the domain size, the number of parties, and the security parameter is essentially tight. Using a reduction of Balle et al. (2019), our improved analysis of the protocol of Ishai et al. yields, in the same model, an $\left(\varepsilon, δ\right)$-differentially private protocol for aggregation that, for any constant $\varepsilon > 0$ and any $δ= \frac{1}{\mathrm{poly}(n)}$, incurs only a constant error and requires only a constant number of messages per party. Previously, such a protocol was known only for $Ω(\log n)$ messages per party.

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