相关论文: Optimizing over Multiple Distributions under Gener…
We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Specifically, we map the simplex to the positive quadrant of a…
We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions. This structure arises in several optimization problems in statistics and machine learning, e.g., for matrix scaling,…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
We develop a novel and single-loop variance-reduced algorithm to solve a class of stochastic nonconvex-convex minimax problems involving a nonconvex-linear objective function, which has various applications in different fields such as…
The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…
This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem,…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed…
The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in…
Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…
We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and…
A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This model is motivated by applications in molecular microscopy and image processing, where each…
In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…