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The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but…
The study of multi-task learning has drawn great attention from the community. Despite the remarkable progress, the challenge of optimally learning different tasks simultaneously remains to be explored. Previous works attempt to modify the…
Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…
Stochastic gradient descent (SGD) is one of the most widely used optimization methods for solving various machine learning problems. SGD solves an optimization problem by iteratively sampling a few data points from the input data, computing…
In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the…
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…
Parameterized feedforward control is at the basis of many successful control applications with varying references. The aim of this paper is to develop an efficient data-driven approach to learn the feedforward parameters for MIMO systems.…
Multi-task learning aims to boost the generalization performance of multiple related tasks simultaneously by leveraging information contained in those tasks. In this paper, we propose a multi-task learning framework, where we utilize prior…
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA)…
Contraction Clustering (RASTER) is a single-pass algorithm for density-based clustering of 2D data. It can process arbitrary amounts of data in linear time and in constant memory, quickly identifying approximate clusters. It also exhibits…
Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification,…
Many large-scale optimization problems can be expressed as composite optimization models. Accelerated first-order methods such as the fast iterative shrinkage-thresholding algorithm (FISTA) have proven effective for numerous large composite…
Large-scale problems in data science are often modeled with optimization, and the optimization model is usually solved with first-order methods that may converge at a sublinear rate. Therefore, it is of interest to terminate the…
In the field of bioimaging, an important part of analyzing the motion of objects is tracking. We propose a method that applies the Sinkhorn distance for solving the optimal transport problem to track objects. The advantage of this method is…
Existing gradient-based optimization methods update parameters locally, in a direction that minimizes the loss function. We study a different approach, symmetry teleportation, that allows parameters to travel a large distance on the loss…
Discrete optimization is a central problem in mathematical optimization with a broad range of applications, among which binary optimization and sparse optimization are two common ones. However, these problems are NP-hard and thus difficult…
The design of novel algorithms for solving inverse problems in signal processing is an incredibly difficult, heuristic-driven, and time-consuming task. In this short paper, we the idea of automated algorithm discovery in the signal…
It is promising to solve linear inverse problems by unfolding iterative algorithms (e.g., iterative shrinkage thresholding algorithm (ISTA)) as deep neural networks (DNNs) with learnable parameters. However, existing ISTA-based unfolded…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-nineties, SIESTA's flexibility, efficiency and free distribution has given advanced materials simulation…