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Towards Deep Learning Models Resistant to Adversarial Attacks
- A. Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, Adrian Vladu
- Computer ScienceICLR
- 19 June 2017
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.
Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods
- Michael B. Cohen, A. Madry, Dimitris Tsipras, Adrian Vladu
- Computer ScienceIEEE 58th Annual Symposium on Foundations of…
- 7 April 2017
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.
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 on…
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.
Tight Bounds for Approximate Carathéodory and Beyond
- V. Mirrokni, Renato Paes Leme, Adrian Vladu, Sam Chiu-wai Wong
- Mathematics, Computer ScienceICML
- 1 December 2015
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 $p \geq 2$.
Circulation Control for Faster Minimum Cost Flow in Unit-Capacity Graphs
- Kyriakos Axiotis, Aleksander Mkadry, Adrian Vladu
- Computer ScienceIEEE 61st Annual Symposium on Foundations of…
- 10 March 2020
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.
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.
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 exclusively…
Decomposable Submodular Function Minimization via Maximum Flow
- Kyriakos Axiotis, Adam Karczmarz, A. Mukherjee, P. Sankowski, Adrian Vladu
- Mathematics, Computer ScienceICML
- 5 March 2021
This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times…
Submodular maximization with matroid and packing constraints in parallel
The first algorithms with low adaptivity for submodular maximization with a matroid constraint are obtained, and the first parallel algorithm for non-monotone submodularity maximization subject to packing constraints is obtained.