Differentially Private Accelerated Optimization Algorithms

We present two classes of differentially private optimization algorithms derived from the well-known accelerated first-order methods. The first algorithm is inspired by Polyak's heavy ball method and employs a smoothing approach to decrease the accumulated noise on the gradient steps required for differential privacy. The second class of algorithms are based on Nesterov's accelerated gradient method and its recent multi-stage variant. We propose a noise dividing mechanism for the iterations of Nesterov's method in order to improve the error behavior of the algorithm. The convergence rate analyses are provided for both the heavy ball and the Nesterov's accelerated gradient method with the help of the dynamical system analysis techniques. Finally, we conclude with our numerical experiments showing that the presented algorithms have advantages over the well-known differentially private algorithms.Comment: 28 pages, 4 figure

Novel gradient-based methods for data distribution and privacy in data science

With an increase in the need of storing data at different locations, designing algorithms that can analyze distributed data is becoming more important. In this thesis, we present several gradient-based algorithms, which are customized for data distribution and privacy. First, we propose a provably convergent, second order incremental and inherently parallel algorithm. The proposed algorithm works with distributed data. By using a local quadratic approximation, we achieve to speed-up the convergence with the help of curvature information. We also illustrate that the parallel implementation of our algorithm performs better than a parallel stochastic gradient descent method to solve a large-scale data science problem. This first algorithm solves the problem of using data that resides at different locations. However, this setting is not necessarily enough for data privacy. To guarantee the privacy of the data, we propose differentially private optimization algorithms in the second part of the thesis. The first one among them employs a smoothing approach which is based on using the weighted averages of the history of gradients. This approach helps to decrease the variance of the noise. This reduction in the variance is important for iterative optimization algorithms, since increasing the amount of noise in the algorithm can harm the performance. We also present differentially private version of a recent multistage accelerated algorithm. These extensions use noise related parameter selection and the proposed stepsizes are proportional to the variance of the noisy gradient. The numerical experiments show that our algorithms show a better performance than some well-known differentially private algorithm

Decentralized Differentially Private Without-Replacement Stochastic Gradient Descent

While machine learning has achieved remarkable results in a wide variety of domains, the training of models often requires large datasets that may need to be collected from different individuals. As sensitive information may be contained in the individual's dataset, sharing training data may lead to severe privacy concerns. Therefore, there is a compelling need to develop privacy-aware machine learning methods, for which one effective approach is to leverage the generic framework of differential privacy. Considering that stochastic gradient descent (SGD) is one of the mostly adopted methods for large-scale machine learning problems, two decentralized differentially private SGD algorithms are proposed in this work. Particularly, we focus on SGD without replacement due to its favorable structure for practical implementation. In addition, both privacy and convergence analysis are provided for the proposed algorithms. Finally, extensive experiments are performed to verify the theoretical results and demonstrate the effectiveness of the proposed algorithms

Crowd-ML: A Privacy-Preserving Learning Framework for a Crowd of Smart Devices

Smart devices with built-in sensors, computational capabilities, and network connectivity have become increasingly pervasive. The crowds of smart devices offer opportunities to collectively sense and perform computing tasks in an unprecedented scale. This paper presents Crowd-ML, a privacy-preserving machine learning framework for a crowd of smart devices, which can solve a wide range of learning problems for crowdsensing data with differential privacy guarantees. Crowd-ML endows a crowdsensing system with an ability to learn classifiers or predictors online from crowdsensing data privately with minimal computational overheads on devices and servers, suitable for a practical and large-scale employment of the framework. We analyze the performance and the scalability of Crowd-ML, and implement the system with off-the-shelf smartphones as a proof of concept. We demonstrate the advantages of Crowd-ML with real and simulated experiments under various conditions