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We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…

Stochastic parametrisations are used in weather and climate models to improve the representation of unpredictable unresolved processes. When compared to a deterministic model, a stochastic model represents `model uncertainty', i.e., sources…

This paper introduces the multiplicative variant of the recently proposed asynchronous additive coarse-space correction method. Definition of an asynchronous extension of multiplicative correction is not straightforward, however, our…

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…

State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. By enforcing such representation to be sparse, sparse subspace clustering is…

This article presents a dynamic regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem…

Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…

In dynamic systems that adapt to users' needs and changing environments, dependability needs cannot be avoided. This paper proposes an orthogonal fault tolerance model as a means to manage and reason about multiple fault tolerance…

We consider stochastic convex optimization problems, where several machines act asynchronously in parallel while sharing a common memory. We propose a robust training method for the constrained setting and derive non asymptotic convergence…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…

Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to…

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…

We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each…

We present techniques that improve the performance of asymmetric stabilizer codes in the presence of unital channels with unknown parameters. Our method estimates the channel parameters using information recovered from syndrome measurements…