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We study a stochastically perturbed version of the well-known Krasnoselski--Mann iteration for computing fixed points of nonexpansive maps in finite dimensional normed spaces. We discuss sufficient conditions on the stochastic noise and…
We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework…
Given points from an arbitrary metric space and a sequence of point updates sent by an adversary, what is the minimum recourse per update (i.e., the minimum number of changes needed to the set of centers after an update), in order to…
A left-corner parsing algorithm with top-down filtering has been reported to show very efficient performance for unification-based systems. However, due to the nontermination of parsing with left-recursive grammars, top-down constraints…
Maintaining a dynamic $k$-core decomposition is an important problem that identifies dense subgraphs in dynamically changing graphs. Recent work by Liu et al. [SPAA 2022] presents a parallel batch-dynamic algorithm for maintaining an…
Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong convergence) of the associated method with both perturbation and…
Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited…
Coresets are modern data-reduction tools that are widely used in data analysis to improve efficiency in terms of running time, space and communication complexity. Our main result is a fast algorithm to construct a small coreset for k-Median…
Motivated by recent advances in serverless cloud computing, in particular the "function as a service" (FaaS) model, we consider the problem of minimizing a convex function in a massively parallel fashion, where communication between workers…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points…
High-Order, High-Dimension, and Sparse Tensor (HOHDST) data originates from real industrial applications, i.e., social networks, recommender systems, bio-information, and traffic information. Sparse Tensor Decomposition (STD) can project…
Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are…
Topological self-stabilization describes the ability of a distributed system to let the nodes themselves establish a meaningful overlay network. Independent from the initial network topology, the system converges to the desired topology via…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
We propose a distributed bootstrap method for simultaneous inference on high-dimensional massive data that are stored and processed with many machines. The method produces an $\ell_\infty$-norm confidence region based on a…
The stochastic momentum method is a commonly used acceleration technique for solving large-scale stochastic optimization problems in artificial neural networks. Current convergence results of stochastic momentum methods under non-convex…
We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…
We introduce a memory- and compute-efficient method for low-communication distributed training. Existing methods reduce communication by performing multiple local updates between infrequent global synchronizations. We demonstrate that their…