Related papers: Convergence of Adaptive, Randomized, Iterative Lin…

We prove ``effective'' linear response for certain classes of non-uniformly expanding random dynamical systems which are not necessarily composed in an i.i.d manner. In applications, the results are obtained for base maps with a sufficient…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…

Although most scheduling problems are NP-hard, domain specific techniques perform well in practice but are quite expensive to construct. In adaptive problem-solving solving, domain specific knowledge is acquired automatically for a general…

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…

Optimisation problems, particularly combinatorial optimisation problems, are difficult to solve due to their complexity and hardness. Such problems have been successfully solved by evolutionary and swarm intelligence algorithms, especially…

Algorithmic recourse seeks to provide actionable recommendations for individuals to overcome unfavorable classification outcomes from automated decision-making systems. Recourse recommendations should ideally be robust to reasonably small…

In the stochastic submodular cover problem, the goal is to select a subset of stochastic items of minimum expected cost to cover a submodular function. Solutions in this setting correspond to sequential decision processes that select items…

Solving linear systems of equations is a fundamental problem in mathematics. When the linear system is so large that it cannot be loaded into memory at once, iterative methods such as the randomized Kaczmarz method excel. Here, we extend…

Collaborative working is increasingly popular, but it presents challenges due to the need for high responsiveness and disconnected work support. To address these challenges the data is optimistically replicated at the edges of the network,…

Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…

We derive a new adaptive leverage score sampling strategy for solving the Column Subset Selection Problem (CSSP). The resulting algorithm, called Adaptive Randomized Pivoting, can be viewed as a randomization of Osinsky's recently proposed…

This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…

Previous papers have shown the impact of partial convergence of discretized PDE on the accuracy of tangent and adjoint linearizations. A series of papers suggested linearization of the fixed point iteration used in the solution process as a…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…