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We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…

Optimization and Control · Mathematics 2022-11-08 Ningning Han , Juan Nie , Jian Lu , Michael K. Ng

The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…

Numerical Analysis · Mathematics 2016-02-11 Silvia Noschese , Lothar Reichel

Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…

Machine Learning · Computer Science 2019-12-24 Jie Chen , Ronny Luss

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of $N$ items. They have recently gained prominence in several applications that rely on "diverse" subsets. However, their applicability to large…

Machine Learning · Computer Science 2016-05-27 Zelda Mariet , Suvrit Sra

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

Machine Learning · Statistics 2021-03-08 Nicole Mücke

Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs offer tractable algorithms…

Machine Learning · Computer Science 2012-02-20 Alex Kulesza , Ben Taskar

The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…

Numerical Analysis · Mathematics 2022-08-16 Rosemary A. Renaut , Anthony W. Helmstetter , Saeed Vatankhah

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…

Machine Learning · Computer Science 2012-07-03 Haim Avron , Satyen Kale , Shiva Kasiviswanathan , Vikas Sindhwani

This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…

Signal Processing · Electrical Eng. & Systems 2020-03-26 Xiao Fu , Shahana Ibrahim , Hoi-To Wai , Cheng Gao , Kejun Huang

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…

Optimization and Control · Mathematics 2015-10-27 Saeed Ghadimi , Guanghui Lan

Topology optimization under uncertainty (TOuU) often defines objectives and constraints by statistical moments of geometric and physical quantities of interest. Most traditional TOuU methods use gradient-based optimization algorithms and…

Optimization and Control · Mathematics 2019-11-05 Subhayan De , Jerrad Hampton , Kurt Maute , Alireza Doostan

In this paper we introduce a family of stochastic gradient estimation techniques based of the perturbative expansion around the mean of the sampling distribution. We characterize the bias and variance of the resulting Taylor-corrected…

Machine Learning · Statistics 2019-11-18 Luca Ambrogioni , Marcel A. J. van Gerven

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Optimization and Control · Mathematics 2019-04-30 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…

Machine Learning · Computer Science 2020-10-20 Dongruo Zhou , Pan Xu , Quanquan Gu

Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…

Optimization and Control · Mathematics 2023-09-06 Stefano Di Giovacchino , Desmond J. Higham , Konstantinos Zygalakis

We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…

Programming Languages · Computer Science 2023-01-10 Basim Khajwal , C. -H. Luke Ong , Dominik Wagner

The paper considers distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents' local expectation-valued convex cost functions. Due to the stochasticity in gradient…

Optimization and Control · Mathematics 2022-04-07 Jinlong Lei , Peng Yi , Jie Chen , Yiguang Hong

This paper proposes a distributed stochastic projection-free algorithm for large-scale constrained finite-sum optimization whose constraint set is complicated such that the projection onto the constraint set can be expensive. The global…

Optimization and Control · Mathematics 2022-04-25 Xia Jiang , Xianlin Zeng , Lihua Xie , Jian Sun , Jie Chen

Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…

Optimization and Control · Mathematics 2020-10-20 Hamza Cherkaoui , Jeremias Sulam , Thomas Moreau

We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…

Optimization and Control · Mathematics 2020-12-22 Andrzej Ruszczynski