Related papers: Data-Dependent Complexity of First-Order Methods f…

Decentralized optimization algorithms have attracted intensive interests recently, as it has a balanced communication pattern, especially when solving large-scale machine learning problems. Stochastic Path Integrated Differential Estimator…

In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-order case, we propose a framework of transition from deterministic or…

Accelerated proximal gradient methods, which are also called fast iterative shrinkage-thresholding algorithms (FISTA) are known to be efficient for many applications. Recently, Tanabe et al. proposed an extension of FISTA for multiobjective…

In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain…

We present TWIST, a simple and theoretically explainable self-supervised representation learning method by classifying large-scale unlabeled datasets in an end-to-end way. We employ a siamese network terminated by a softmax operation to…

We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…

We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates a class of cut selection…

We design an algorithm which finds an $\epsilon$-approximate stationary point (with $\|\nabla F(x)\|\le \epsilon$) using $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector products, matching guarantees that were previously available…

We propose a First-Order System Least Squares (FOSLS) method based on deep-learning for numerically solving second-order elliptic PDEs. The method we propose is capable of dealing with either variational and non-variational problems, and…

Hierarchical least-squares programming (HLSP) is an important tool in optimization as it enables the stacking of any number of priority levels in order to reflect complex constraint relationships, for example in physical systems like…

Support Vector Machines (SVMs) are among the most fundamental tools for binary classification. In its simplest formulation, an SVM produces a hyperplane separating two classes of data using the largest possible margin to the data. The focus…

This paper presents a first-order distributed algorithm for solving a convex semi-infinite program (SIP) over a time-varying network. In this setting, the objective function associated with the optimization problem is a summation of a set…

A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…

We study the problem of fine-tuning a language model (LM) for a target task by optimally using the information from $n$ auxiliary tasks. This problem has broad applications in NLP, such as targeted instruction tuning and data selection in…

Time-sensitive machine learning benefits from Sequential Probability Ratio Test (SPRT), which provides an optimal stopping time for early classification of time series. However, in finite horizon scenarios, where input lengths are finite,…

We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…

We consider the optimization problem of minimizing the logistic loss with gradient descent to train a linear model for binary classification with separable data. With a budget of $T$ iterations, it was recently shown that an accelerated…

In this paper we propose a stochastic primal dual fixed point method (SPDFP) for solving the sum of two proper lower semi-continuous convex function and one of which is composite. The method is based on the primal dual fixed point method…

Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…

We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation…