Federated Learning (FL) is a promising machine learning paradigm that enables the analyzer to train a model without collecting users' raw data. To ensure users' privacy, differentially private federated learning has been intensively studied. The existing works are mainly based on the \textit{curator model} or \textit{local model} of differential privacy. However, both of them have pros and cons. The curator model allows greater accuracy but requires a trusted analyzer. In the local model where users randomize local data before sending them to the analyzer, a trusted analyzer is not required but the accuracy is limited. In this work, by leveraging the \textit{privacy amplification} effect in the recently proposed shuffle model of differential privacy, we achieve the best of two worlds, i.e., accuracy in the curator model and strong privacy without relying on any trusted party. We first propose an FL framework in the shuffle model and a simple protocol (SS-Simple) extended from existing work. We find that SS-Simple only provides an insufficient privacy amplification effect in FL since the dimension of the model parameter is quite large. To solve this challenge, we propose an enhanced protocol (SS-Double) to increase the privacy amplification effect by subsampling. Furthermore, for boosting the utility when the model size is greater than the user population, we propose an advanced protocol (SS-Topk) with gradient sparsification techniques. We also provide theoretical analysis and numerical evaluations of the privacy amplification of the proposed protocols. Experiments on real-world dataset validate that SS-Topk improves the testing accuracy by 60.7\% than the local model based FL.
The shuffle model of differential privacy was proposed as a viable model for performing distributed differentially private computations. Informally, the model consists of an untrusted analyzer that receives messages sent by participating parties via a shuffle functionality, the latter potentially disassociates messages from their senders. Prior work focused on one-round differentially private shuffle model protocols, demonstrating that functionalities such as addition and histograms can be performed in this model with accuracy levels similar to that of the curator model of differential privacy…
Google Research（谷歌研究院）；IT University of Copenhagen（哥本哈根信息技术大学）
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 s…
In recent work, Cheu et al. (Eurocrypt 2019) proposed a protocol for $n$-party real summation in the shuffle model of differential privacy with $O_{ε, δ}(1)$ error and $Θ(ε\sqrt{n})$ one-bit messages per party. In contrast, every local model protocol for real summation must incur error $Ω(1/\sqrt{n})$, and there exist protocols matching this lower bound which require just one bit of communication per party. Whether this gap in number of messages is necessary was left open by Cheu et al. In this note we show a protocol with $O(1/ε)$ error and $O(\log(n/δ))$ messages of size $O(\log(n))$ per par…
In this paper, we propose differentially private algorithms for the problem of stochastic linear bandits in the central, local and shuffled models. In the central model, we achieve almost the same regret as the optimal non-private algorithms, which means we get privacy for free. In particular, we achieve a regret of $\tilde{O}(\sqrt{T}+\frac{1}ε)$ matching the known lower bound for private linear bandits, while the best previously known algorithm achieves $\tilde{O}(\frac{1}ε\sqrt{T})$. In the local case, we achieve a regret of $\tilde{O}(\frac{1}ε{\sqrt{T}})$ which matches the non-private reg…
Beyond Statistical Estimation: Differentially Private Individual Computation via Shuffling
Guangzhou University（广州大学）；National University of Singapore（新加坡国立大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；University of Southampton（南安普顿大学）
Google Research（谷歌研究院）；Tel Aviv University（特拉维夫大学）
We introduce the concurrent shuffle model of differential privacy. In this model we have multiple concurrent shufflers permuting messages from different, possibly overlapping, batches of users. Similarly to the standard (single) shuffle model, the privacy requirement is that the concatenation of all shuffled messages should be differentially private. We study the private continual summation problem (a.k.a. the counter problem) and show that the concurrent shuffle model allows for significantly improved error compared to a standard (single) shuffle model. Specifically, we give a summation algor…
The central question studied in this paper is Renyi Differential Privacy (RDP) guarantees for general discrete local mechanisms in the shuffle privacy model. In the shuffle model, each of the $n$ clients randomizes its response using a local differentially private (LDP) mechanism and the untrusted server only receives a random permutation (shuffle) of the client responses without association to each client. The principal result in this paper is the first non-trivial RDP guarantee for general discrete local randomization mechanisms in the shuffled privacy model, and we develop new analysis tech…
We study differentially private distributed optimization under communication constraints. A server using SGD for optimization aggregates the client-side local gradients for model updates using distributed mean estimation (DME). We develop a communication-efficient private DME, using the recently developed multi-message shuffled (MMS) privacy framework. We analyze our proposed DME scheme to show that it achieves the order-optimal privacy-communication-performance tradeoff resolving an open question in [1], whether the shuffled models can improve the tradeoff obtained in Secure Aggregation. This…
Prior work on differential privacy analysis of randomized SGD algorithms relies on composition theorems, where the implicit (unrealistic) assumption is that the internal state of the iterative algorithm is revealed to the adversary. As a result, the Rényi DP bounds derived by such composition-based analyses linearly grow with the number of training epochs. When the internal state of the algorithm is hidden, we prove a converging privacy bound for noisy stochastic gradient descent (on strongly convex smooth loss functions). We show how to take advantage of privacy amplification by sub-sampling …
We study privacy in a distributed learning framework, where clients collaboratively build a learning model iteratively through interactions with a server from whom we need privacy. Motivated by stochastic optimization and the federated learning (FL) paradigm, we focus on the case where a small fraction of data samples are randomly sub-sampled in each round to participate in the learning process, which also enables privacy amplification. To obtain even stronger local privacy guarantees, we study this in the shuffle privacy model, where each client randomizes its response using a local different…
Google Research（谷歌研究院）；MIT（麻省理工学院）；IT University of Copenhagen（哥本哈根信息技术大学）
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 s…
Google Research（谷歌研究院）；Tel Aviv University（特拉维夫大学）
We give an $(\varepsilon,δ)$-differentially private algorithm for the multi-armed bandit (MAB) problem in the shuffle model with a distribution-dependent regret of $O\left(\left(\sum_{a\in [k]:Δ_a>0}\frac{\log T}{Δ_a}\right)+\frac{k\sqrt{\log\frac{1}δ}\log T}{\varepsilon}\right)$, and a distribution-independent regret of $O\left(\sqrt{kT\log T}+\frac{k\sqrt{\log\frac{1}δ}\log T}{\varepsilon}\right)$, where $T$ is the number of rounds, $Δ_a$ is the suboptimality gap of the arm $a$, and $k$ is the total number of arms. Our upper bound almost matches the regret of the best known algorithms for th…
Massachusetts Institute of Technology（麻省理工学院）；Google Research（谷歌研究院）
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 litera…
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…
Recent work of Erlingsson, Feldman, Mironov, Raghunathan, Talwar, and Thakurta [EFMRTT19] demonstrates that random shuffling amplifies differential privacy guarantees of locally randomized data. Such amplification implies substantially stronger privacy guarantees for systems in which data is contributed anonymously [BEMMRLRKTS17] and has lead to significant interest in the shuffle model of privacy [CSUZZ19; EFMRTT19]. We show that random shuffling of $n$ data records that are input to $\varepsilon_0$-differentially private local randomizers results in an $(O((1-e^{-\varepsilon_0})\sqrt{\frac{e…
Near-Optimal Reinforcement Learning with Shuffle Differential Privacy
College of Control Science and Engineering, Zhejiang University（控制科学与工程学院，浙江大学）；Department of Computer Science, University of Copenhagen（计算机科学系，哥本哈根大学）
