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Towards Deep Learning Models Resistant to Adversarial Attacks
This work studies the adversarial robustness of neural networks through the lens of robust optimization, and suggests the notion of security against a first-order adversary as a natural and broad security guarantee. Expand
Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods
A new second-order optimization framework is developed that enables the treatment of matrix scaling and balancing in a unified and principled manner and identifies a certain generalization of linear system solving that can be used to efficiently minimize a broad class of functions, which is called second- order robust. Expand
Improved Parallel Algorithms for Spanners and Hopsets
We use exponential start time clustering to design faster parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions onExpand
Tight Bounds for Approximate Carathéodory and Beyond
The result provides a constructive proof for the Approximate Carath-eodory Problem, which states that any point inside a polytope contained in the ball of radius $D$ can be approximated to within $\epsilon$ in $\ell_p$ norm by a convex combination of only $O\left(D^2 p/\ep silon^2\right)$ vertices of the polytopes for $p \geq 2$. Expand
Almost-linear-time algorithms for Markov chains and new spectral primitives for directed graphs
The first almost-linear-time directed Laplacian system solver is designed, a notion of approximation is provided for directed graphs, and sparsifiers under this notion always exist are proved. Expand
Circulation Control for Faster Minimum Cost Flow in Unit-Capacity Graphs
This work obtains a faster algorithm for solving the minimum cost flow problem in graphs with unit capacity by combining a regularized version of the standard Newton step with a customized preconditioning method which aims to ensure that the graph on which these circulations are computed has sufficiently large conductance. Expand
Improved Convergence for and 1 Regression via Iteratively Reweighted Least Squares
We use weightings of A’s columns c 2 Rm which we refer to as conductances. We equivalently refer to the reciprocals r 2 Rm, with r i = 1/ci, which we call resistances. Our analysis is exclusivelyExpand
Negative-Weight Shortest Paths and Unit Capacity Minimum Cost Flow in Õ(m 10/7 log W) Time.
In this paper, we study a set of combinatorial optimization problems on weighted graphs: the shortest path problem with negative weights, the weighted perfect bipartite matching problem, theExpand
Faster Algorithms for Computing the Stationary Distribution, Simulating Random Walks, and More
This paper provides faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape probabilities, and shows how to compute each quantity in time Õ(m3/4n + mn2/3), where the Ó notation suppresses polylog factors in n. Expand
Multidimensional Binary Search for Contextual Decision-Making
This work considers a multidimensional search problem that is motivated by questions in contextual decision-making, such as dynamic pricing and personalized medicine, and constructs a polynomial time algorithm that is optimal up to a logd factor. Expand