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We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
We study the convergence of the last iterate in subgradient methods applied to the minimization of a nonsmooth convex function with bounded subgradients. We first introduce a proof technique that generalizes the standard analysis of…
In many distributed learning problems, the heterogeneous loading of computing machines may harm the overall performance of synchronous strategies. In this paper, we propose an effective asynchronous distributed framework for the…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Mini-batch optimization has proven to be a powerful paradigm for large-scale learning. However, the state of the art parallel mini-batch algorithms assume synchronous operation or cyclic update orders. When worker nodes are heterogeneous…
We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually each…
We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
We provide an algorithm that maintains, against an adaptive adversary, a $(1-\varepsilon)$-approximate maximum matching in $n$-node $m$-edge general (not necessarily bipartite) undirected graph undergoing edge deletions with high…
In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…
We study the distributed consensus of state vectors in a discrete-time multi-agent network with matrix edge weights using stochastic matrix convergence theory. We present a distributed asynchronous time update model wherein one randomly…
We adapt a well known streaming algorithm for approximating item frequencies to the matrix sketching setting. The algorithm receives the rows of a large matrix $A \in \R^{n \times m}$ one after the other in a streaming fashion. It maintains…
In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate…
We study the convergence of stochastic fixed point iterations in the consistent case (in the sense of Butnariu and Fl{\aa}m (1995)) in several different settings, under decreasingly restrictive regularity assumptions of the fixed point…
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…
We describe a new algorithm called Frequent Directions for deterministic matrix sketching in the row-updates model. The algorithm is presented an arbitrary input matrix $A \in R^{n \times d}$ one row at a time. It performed $O(d \times…
We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erd\H{o}s-R\'enyi graphs. Our error bounds are sharp for a large class of sparse random matrices.…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is…