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This paper studies a class of distributed optimization algorithms by a set of agents, where each agent has only access to its own local convex objective function, and jointly minimizes the sum of the functions. The communications among…
Graph Balancing is the problem of orienting the edges of a weighted multigraph so as to minimize the maximum weighted in-degree. Since the introduction of the problem the best algorithm known achieves an approximation ratio of $1.75$ and it…
We study a family of algorithms, which we refer to as local update methods, that generalize many federated learning and meta-learning algorithms. We prove that for quadratic objectives, local update methods perform stochastic gradient…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error…
We consider decentralized machine learning over a network where the training data is distributed across $n$ agents, each of which can compute stochastic model updates on their local data. The agent's common goal is to find a model that…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
We investigate structural properties of large, sparse random graphs through the lens of "sampling convergence" (Borgs et. al. (2017)). Sampling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a…
In federated distributed learning, the goal is to optimize a global training objective defined over distributed devices, where the data shard at each device is sampled from a possibly different distribution (a.k.a., heterogeneous or non…
This paper provides a comprehensive and detailed analysis of the local convergence behavior of an extended variation of the locally optimal preconditioned conjugate gradient method (LOBPCG) for computing the extreme eigenvalue of a…
Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…
Gradient sensing requires at least two measurements at different points in space. These measurements must then be communicated to a common location to be compared, which is unavoidably noisy. While much is known about the limits of…
In this paper, based on the limited memory techniques and subspace minimization conjugate gradient (SMCG) methods, a regularized limited memory subspace minimization conjugate gradient method is proposed, which contains two types of…
The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…
This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the…
To accelerate the training of graph convolutional networks (GCNs) on real-world large-scale sparse graphs, downsampling methods are commonly employed as a preprocessing step. However, the effects of graph sparsity and topological structure…
In this work, we showed that the Implicit Update and Predictive Methods dynamics introduced in prior work satisfy last iterate convergence to a neighborhood around the optimum in overparameterized GANs, where the size of the neighborhood…
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…