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Deep learning-based numerical schemes for solving high-dimensional backward stochastic differential equations (BSDEs) have recently raised plenty of scientific interest. While they enable numerical methods to approximate very…

In many applications involving large dataset or online updating, stochastic gradient descent (SGD) provides a scalable way to compute parameter estimates and has gained increasing popularity due to its numerical convenience and memory…

Differentially Private Stochastic Gradient Descent (DP-SGD) is widely used to protect training data in machine learning. Its privacy guarantee is commonly analyzed through a security game in which an adversary infers whether a target record…

Stochastic optimization is a pivotal enabler in modern machine learning, producing effective models for various tasks. However, several existing works have shown that model parameters and gradient information are susceptible to privacy…

Differential privacy (DP) is a popular mechanism for training machine learning models with bounded leakage about the presence of specific points in the training data. The cost of differential privacy is a reduction in the model's accuracy.…

Differentially private stochastic gradient descent (DP-SGD) is the canonical approach to private deep learning. While the current privacy analysis of DP-SGD is known to be tight in some settings, several empirical results suggest that…

Distributed stochastic gradient descent is an important subroutine in distributed learning. A setting of particular interest is when the clients are mobile devices, where two important concerns are communication efficiency and the privacy…

Bayesian neural network (BNN) allows for uncertainty quantification in prediction, offering an advantage over regular neural networks that has not been explored in the differential privacy (DP) framework. We fill this important gap by…

Differential privacy is a useful tool to build machine learning models which do not release too much information about the training data. We study the R\'enyi differential privacy of stochastic gradient descent when each training example is…

The interplay between optimization and privacy has become a central theme in privacy-preserving machine learning. Noisy stochastic gradient descent (SGD) has emerged as a cornerstone algorithm, particularly in large-scale settings. These…

In this paper, we investigate federated learning for quantile inference under local differential privacy (LDP). We propose an estimator based on local stochastic gradient descent (SGD), whose local gradients are perturbed via a randomized…

Differentially private (DP) mechanisms protect individual-level information by introducing randomness into the statistical analysis procedure. Despite the availability of numerous DP tools, there remains a lack of general techniques for…

Machine learning models are known to memorize private data to reduce their training loss, which can be inadvertently exploited by privacy attacks such as model inversion and membership inference. To protect against these attacks,…

In this paper some methods to use the empirical bootstrap approach for stochastic gradient descent (SGD) to minimize the empirical risk over a separable Hilbert space are investigated from the view point of algorithmic stability and…

Communication efficiency and privacy protection are two critical issues in distributed machine learning. Existing methods tackle these two issues separately and may have a high implementation complexity that constrains their application in…

Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…

The vanilla Differentially-Private Stochastic Gradient Descent (DP-SGD), including DP-Adam and other variants, ensures the privacy of training data by uniformly distributing privacy costs across training steps. The equivalent privacy costs…

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

The Noisy-SGD algorithm is widely used for privately training machine learning models. Traditional privacy analyses of this algorithm assume that the internal state is publicly revealed, resulting in privacy loss bounds that increase…

Despite the popularity of Convolutional Neural Networks (CNN), the problem of uncertainty quantification (UQ) of CNN has been largely overlooked. Lack of efficient UQ tools severely limits the application of CNN in certain areas, such as…