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1. Recycled ADMM: Improve Privacy and Accuracy with Less Computation in Distributed Algorithms

   Zhang, Xueru; Khalili, Mohammad Mahdi; Liu, Mingyan (January 2018, Annual Allerton Conference on Control, Communication, and Computing)

   Alternating direction method of multiplier (ADMM) is a powerful method to solve decentralized convex optimization problems. In distributed settings, each node performs computation with its local data and the local results are exchanged among neighboring nodes in an iterative fashion. During this iterative process the leakage of data privacy arises and can accumulate significantly over many iterations, making it difficult to balance the privacy-utility tradeoff. In this study we propose Recycled ADMM (R-ADMM), where a linear approximation is applied to every even iteration, its solution directly calculated using only results from the previous, odd iteration. It turns out that under such a scheme, half of the updates incur no privacy loss and require much less computation compared to the conventional ADMM. We obtain a sufficient condition for the convergence of R-ADMM and provide the privacy analysis based on objective perturbation. 

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2. 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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3. Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series

   https://doi.org/10.1109/ICASSP43922.2022.9747446  

   Tugnait, Jitendra K. (May 2022, ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |)

   We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso based frequency-domain formulation of the problem has been considered in the literature where the objective is to estimate the sparse inverse power spectral density (PSD) of the data. The CIG is then inferred from the estimated inverse PSD. In this paper we investigate use of a sparse-group log-sum penalty (LSP) instead of sparse-group lasso penalty. An alternating direction method of multipliers (ADMM) approach for iterative optimization of the non-convex problem is presented. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This results also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data. 

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4. Distributed Learning without Distress: Privacy-Preserving Empirical Risk Minimization

   Bargav Jayaraman, Lingxiao Wang (December 2018, Advances in neural information processing systems)

   Distributed learning allows a group of independent data owners to collaboratively learn a model over their data sets without exposing their private data. We present a distributed learning approach that combines differential privacy with secure multi-party computation. We explore two popular methods of differential privacy, output perturbation and gradient perturbation, and advance the state-of-the-art for both methods in the distributed learning setting. In our output perturbation method, the parties combine local models within a secure computation and then add the required differential privacy noise before revealing the model. In our gradient perturbation method, the data owners collaboratively train a global model via an iterative learning algorithm. At each iteration, the parties aggregate their local gradients within a secure computation, adding sufficient noise to ensure privacy before the gradient updates are revealed. For both methods, we show that the noise can be reduced in the multi-party setting by adding the noise inside the secure computation after aggregation, asymptotically improving upon the best previous results. Experiments on real world data sets demonstrate that our methods provide substantial utility gains for typical privacy requirements. 

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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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