Related papers: Randomized Kaczmarz in Adversarial Distributed Set…

In this paper, for solving inconsistent matrix equations we propose a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum. Without the full column rank assumptions on coefficient matrices, we…

The susceptibility of modern machine learning classifiers to adversarial examples has motivated theoretical results suggesting that these might be unavoidable. However, these results can be too general to be applicable to natural data…

Randomized Kaczmarz-type methods are widely used for their simplicity and efficiency in solving large-scale linear systems and optimization problems. However, their applicability is limited when dealing with inconsistent systems or…

We consider an adversarially-trained version of the nonnegative matrix factorization, a popular latent dimensionality reduction technique. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We…

Randomized linear solvers randomly compress and solve a linear system with compelling theoretical convergence rates and computational complexities. However, such solvers suffer a substantial disconnect between their theoretical rates and…

In this paper, we present a dual-layer online optimization strategy for defender robots operating in multiplayer reach-avoid games within general convex environments. Our goal is to intercept as many attacker robots as possible without…

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic…

The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax=b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin…

The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a…

In this letter, we study distributed optimization, where a network of agents, abstracted as a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing approaches over directed graphs are…

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…

We propose a framework for adversarial training that relies on a sample rather than a single sample point as the fundamental unit of discrimination. Inspired by discrepancy measures and two-sample tests between probability distributions, we…

Convolutional neural networks have demonstrated high accuracy on various tasks in recent years. However, they are extremely vulnerable to adversarial examples. For example, imperceptible perturbations added to clean images can cause…

This paper investigates recently proposed approaches for defending against adversarial examples and evaluating adversarial robustness. We motivate 'adversarial risk' as an objective for achieving models robust to worst-case inputs. We then…

As we seek to deploy machine learning models beyond virtual and controlled domains, it is critical to analyze not only the accuracy or the fact that it works most of the time, but if such a model is truly robust and reliable. This paper…

We study the stochastic multi-armed bandits problem in the presence of adversarial corruption. We present a new algorithm for this problem whose regret is nearly optimal, substantially improving upon previous work. Our algorithm is agnostic…

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…