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We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic…

Optimization and Control · Mathematics 2019-06-26 Junyu Zhang , Lin Xiao

This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear…

Machine Learning · Statistics 2017-11-15 Liu Liu , Ji Liu , Dacheng Tao

Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…

Numerical Analysis · Mathematics 2020-06-02 Lu Xia , Martijn Anthonissen , Michiel Hochstenbach , Barry Koren

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…

Optimization and Control · Mathematics 2020-02-28 Derek Driggs , Jingwei Liang , Carola-Bibiane Schönlieb

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. This point of view covers the stochastic gradient…

Machine Learning · Statistics 2019-05-08 Andrei Kulunchakov , Julien Mairal

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of…

Machine Learning · Statistics 2020-09-07 Andrei Kulunchakov , Julien Mairal

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…

Machine Learning · Statistics 2026-05-26 Mohammadreza Ahmadypour , Tara Javidi , Farinaz Koushanfar

In this note we propose a new variant of the hybrid variance-reduced proximal gradient method in [7] to solve a common stochastic composite nonconvex optimization problem under standard assumptions. We simply replace the independent…

Optimization and Control · Mathematics 2020-08-21 Deyi Liu , Lam M. Nguyen , Quoc Tran-Dinh

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…

Machine Learning · Statistics 2018-02-01 Ke Ma , Jinshan Zeng , Jiechao Xiong , Qianqian Xu , Xiaochun Cao , Wei Liu , Yuan Yao

In this paper, we study the performance of a large family of SGD variants in the smooth nonconvex regime. To this end, we propose a generic and flexible assumption capable of accurate modeling of the second moment of the stochastic…

Optimization and Control · Mathematics 2020-06-15 Zhize Li , Peter Richtárik

In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to…

Computational Finance · Quantitative Finance 2012-07-11 Chang-han Rhee , Peter W. Glynn

Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…

Optimization and Control · Mathematics 2019-01-28 Fabian Pedregosa , Kilian Fatras , Mattia Casotto

The low-rank stochastic semidefinite optimization has attracted rising attention due to its wide range of applications. The nonconvex reformulation based on the low-rank factorization, significantly improves the computational efficiency but…

Optimization and Control · Mathematics 2021-01-05 Jinshan Zeng , Yixuan Zha , Ke Ma , Yuan Yao

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

This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…

Optimization and Control · Mathematics 2025-01-14 Raghu Bollapragada , Cem Karamanli

Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…

Optimization and Control · Mathematics 2019-10-02 Farzad Yousefian , Angelia Nedić , Uday Shanbhag

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are based on semi-definite programming (\textit{SDP}), which is generally…

Machine Learning · Computer Science 2019-12-03 Ke Ma , Jinshan Zeng , Qianqian Xu , Xiaochun Cao , Wei Liu , Yuan Yao

Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased…

Methodology · Statistics 2026-05-14 Matias Quiroz , Aishwarya Bhaskaran , Zixuan Wang , Thomas Goodwin

Variance reduction techniques such as SPIDER/SARAH/STORM have been extensively studied to improve the convergence rates of stochastic non-convex optimization, which usually maintain and update a sequence of estimators for a single function…

Machine Learning · Computer Science 2023-01-02 Wei Jiang , Gang Li , Yibo Wang , Lijun Zhang , Tianbao Yang

Learning low-dimensional latent representations is a central topic in statistics and machine learning, and rotation methods have long been used to obtain sparse and interpretable representations. Despite nearly a century of widespread use…

Methodology · Statistics 2026-02-27 Chengyu Cui , Yunxiao Chen , Jing Ouyang , Gongjun Xu