相关论文: Semi-Implicit Hybrid Gradient Methods with Applica…

Nonconvex-nonconcave minimax optimization has received intense attention over the last decade due to its broad applications in machine learning. Most existing algorithms rely on one-sided information, such as the convexity (resp. concavity)…

Even though deep neural networks succeed on many different tasks including semantic segmentation, they lack on robustness against adversarial examples. To counteract this exploit, often adversarial training is used. However, it is known…

Training neural networks which are robust to adversarial attacks remains an important problem in deep learning, especially as heavily overparameterized models are adopted in safety-critical settings. Drawing from recent work which…

Crafting adversarial examples has become an important technique to evaluate the robustness of deep neural networks (DNNs). However, most existing works focus on attacking the image classification problem since its input space is continuous…

A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…

Robust training methods against perturbations to the input data have received great attention in the machine learning literature. A standard approach in this direction is adversarial training which learns a model using…

This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings --…

We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component,…

Hamilton-Jacobi (HJ) partial differential equations (PDEs) have diverse applications spanning physics, optimal control, game theory, and imaging sciences. This research introduces a first-order optimization-based technique for HJ PDEs,…

Adversarial Training (AT) is one of the most effective methods to enhance the robustness of Deep Neural Networks (DNNs). However, existing AT methods suffer from an inherent accuracy-robustness trade-off. Previous works have studied this…

The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed…

Artifical Neural Networks are a particular class of learning systems modeled after biological neural functions with an interesting penchant for Hebbian learning, that is "neurons that wire together, fire together". However, unlike their…

Gradient descent (GD) and stochastic gradient descent (SGD) are the workhorses of large-scale machine learning. While classical theory focused on analyzing the performance of these methods in convex optimization problems, the most notable…

In practice, deep neural networks have been found to be vulnerable to various types of noise, such as adversarial examples and corruption. Various adversarial defense methods have accordingly been developed to improve adversarial robustness…

We analyze stochastic gradient algorithms for optimizing nonconvex problems. In particular, our goal is to find local minima (second-order stationary points) instead of just finding first-order stationary points which may be some bad…

In this paper we propose several adaptive gradient methods for stochastic optimization. Unlike AdaGrad-type of methods, our algorithms are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of…

Primal-dual algorithms for the resolution of convex-concave saddle point problems usually come with one or several step size parameters. Within the range where convergence is guaranteed, choosing well the step size can make the difference…

Asynchronous parallel implementations of stochastic gradient (SG) have been broadly used in solving deep neural network and received many successes in practice recently. However, existing theories cannot explain their convergence and…

In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a…

Adversarial Training (AT) is one of the most effective methods to train robust Deep Neural Networks (DNNs). However, AT creates an inherent trade-off between clean accuracy and adversarial robustness, which is commonly attributed to the…