Related papers: A midpoint projection algorithm for stochastic dif…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…
We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…
Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon…
A solution manifold is the collection of points in a $d$-dimensional space satisfying a system of $s$ equations with $s<d$. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families,…
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…
We introduce the Projected Push-Pull algorithm that enables multiple agents to solve a distributed constrained optimization problem with private cost functions and global constraints, in a collaborative manner. Our algorithm employs…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
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 distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time-varying connectivity. Our framework is general in that this value can represent a consensus…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…
This paper addresses distributed parameter estimation in stochastic dynamic systems with quantized measurements, constrained by quantized communication and Markovian switching directed topologies. To enable accurate recovery of the original…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Stochastic projection algorithms for solving convex feasibility problems (CFPs) have attracted considerable attention due to their broad applicability. In this paper, we propose a unified stochastic bilevel reformulation for possibly…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
Orthogonality constrained optimization is widely used in applications from science and engineering. Due to the nonconvex orthogonality constraints, many numerical algorithms often can hardly achieve the global optimality. We aim at…