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1. Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learning

   Lamperski, A. (August 2021, Proceedings of Thirty Fourth Conference on Learning Theory)

   Belkin, M.; Kpotufe, S. (Ed.)

   Langevin algorithms are gradient descent methods with additive noise. They have been used for decades in Markov Chain Monte Carlo (MCMC) sampling, optimization, and learning. Their convergence properties for unconstrained non-convex optimization and learning problems have been studied widely in the last few years. Other work has examined projected Langevin algorithms for sampling from log-concave distributions restricted to convex compact sets. For learning and optimization, log-concave distributions correspond to convex losses. In this paper, we analyze the case of non-convex losses with compact convex constraint sets and IID external data variables. We term the resulting method the projected stochastic gradient Langevin algorithm (PSGLA). We show the algorithm achieves a deviation of 𝑂(𝑇−1/4(𝑙𝑜𝑔𝑇)1/2) from its target distribution in 1-Wasserstein distance. For optimization and learning, we show that the algorithm achieves 𝜖-suboptimal solutions, on average, provided that it is run for a time that is polynomial in 𝜖 and slightly super-exponential in the problem dimension. 

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2. Differentially private binary- and matrix-valued data query: an XOR mechanism

   https://doi.org/10.14778/3446095.3446106  

   Ji, Tianxi; Li, Pan; Yilmaz, Emre; Ayday, Erman; Ye, Yanfang; Sun, Jinyuan (January 2021, Proceedings of the VLDB Endowment)

   null (Ed.)

   Differential privacy has been widely adopted to release continuous- and scalar-valued information on a database without compromising the privacy of individual data records in it. The problem of querying binary- and matrix-valued information on a database in a differentially private manner has rarely been studied. However, binary- and matrix-valued data are ubiquitous in real-world applications, whose privacy concerns may arise under a variety of circumstances. In this paper, we devise an exclusive or (XOR) mechanism that perturbs binary- and matrix-valued query result by conducting an XOR operation on the query result with calibrated noises attributed to a matrix-valued Bernoulli distribution. We first rigorously analyze the privacy and utility guarantee of the proposed XOR mechanism. Then, to generate the parameters in the matrix-valued Bernoulli distribution, we develop a heuristic approach to minimize the expected square query error rate under ϵ -differential privacy constraint. Additionally, to address the intractability of calculating the probability density function (PDF) of this distribution and efficiently generate samples from it, we adapt an Exact Hamiltonian Monte Carlo based sampling scheme. Finally, we experimentally demonstrate the efficacy of the XOR mechanism by considering binary data classification and social network analysis, all in a differentially private manner. Experiment results show that the XOR mechanism notably outperforms other state-of-the-art differentially private methods in terms of utility (such as classification accuracy and F 1 score), and even achieves comparable utility to the non-private mechanisms. 

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3. Stochastic ADMM Based Distributed Machine Learning with Differential Privacy

   https://doi.org/10.1007/978-3-030-37228-6_13  

   Ding, Jiahao; Errapotu, Sai Mounika; Zhang, Haijun; Gong, Yanmin; Pan, Miao; Han, Zhu (December 2019, Lecture notes of the Institute for Computer Sciences Social Informatics and Telecommunications Engineering)

   While embracing various machine learning techniques to make effective decisions in the big data era, preserving the privacy of sensitive data poses significant challenges. In this paper, we develop a privacy-preserving distributed machine learning algorithm to address this issue. Given the assumption that each data provider owns a dataset with different sample size, our goal is to learn a common classifier over the union of all the local datasets in a distributed way without leaking any sensitive information of the data samples. Such an algorithm needs to jointly consider efficient distributed learning and effective privacy preservation. In the proposed algorithm, we extend stochastic alternating direction method of multipliers (ADMM) in a distributed setting to do distributed learning. For preserving privacy during the iterative process, we combine differential privacy and stochastic ADMM together. In particular, we propose a novel stochastic ADMM based privacy-preserving distributed machine learning (PS-ADMM) algorithm by perturbing the updating gradients, that provide differential privacy guarantee and have a low computational cost. We theoretically demonstrate the convergence rate and utility bound of our proposed PS-ADMM under strongly convex objective. Through our experiments performed on real-world datasets, we show that PS-ADMM outperforms other differentially private ADMM algorithms under the same differential privacy guarantee. 

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4. Understanding Clipping for Federated Learning: Convergence and Client-Level Differential Privacy

   Xinwei Zhang; Xiangyi Chen; Mingyi Hong; Zhiwei Steven Wu; Jinfeng Yi (July 2022, International Conference on Machine Learning)

   Providing privacy protection has been one of the primary motivations of Federated Learning (FL). Recently, there has been a line of work on incorporating the formal privacy notion of differential privacy with FL. To guarantee the client-level differential privacy in FL algorithms, the clients’ transmitted model updates have to be clipped before adding privacy noise. Such clipping operation is substantially different from its counterpart of gradient clipping in the centralized differentially private SGD and has not been well-understood. In this paper, we first empirically demonstrate that the clipped FedAvg can perform surprisingly well even with substantial data heterogeneity when training neural networks, which is partly because the clients’ updates become similar for several popular deep architectures. Based on this key observation, we provide the convergence analysis of a differential private (DP) FedAvg algorithm and highlight the relationship between clipping bias and the distribution of the clients’ updates. To the best of our knowledge, this is the first work that rigorously investigates theoretical and empirical issues regarding the clipping operation in FL algorithms. 

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5. Shuffled model of differential privacy in federated learnin

   Girgis, Antonious M; Data, Deepesh; Diggavi, Suhas; Kairouz, Peter; and Suresh, Theerta. (January 2021, International Conference on Artificial Intelligence and Statistics, AISTATS)

   We consider a distributed empirical risk minimization (ERM) optimization problem with communication efficiency and privacy requirements, motivated by the federated learn- ing (FL) framework. We propose a distributed communication-efficient and local differentially private stochastic gradient descent (CLDP-SGD) algorithm and analyze its communication, privacy, and convergence trade-offs. Since each iteration of the CLDP- SGD aggregates the client-side local gradients, we develop (optimal) communication-efficient schemes for mean estimation for several lp spaces under local differential privacy (LDP). To overcome performance limitation of LDP, CLDP-SGD takes advantage of the inherent privacy amplification provided by client sub- sampling and data subsampling at each se- lected client (through SGD) as well as the recently developed shuffled model of privacy. For convex loss functions, we prove that the proposed CLDP-SGD algorithm matches the known lower bounds on the centralized private ERM while using a finite number of bits per iteration for each client, i.e., effectively get- ting communication efficiency for “free”. We also provide preliminary experimental results supporting the theory. 

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