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In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…

Optimization and Control · Mathematics 2024-06-05 Taisei Miyaishi , Ryota Nozawa , Pierre-Louis Poirion , Akiko Takeda

We propose a trust-region stochastic sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with stochastic objectives and deterministic equality constraints. We consider a fully stochastic setting,…

Optimization and Control · Mathematics 2024-01-30 Yuchen Fang , Sen Na , Michael W. Mahoney , Mladen Kolar

This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…

Optimization and Control · Mathematics 2024-10-24 Wei Jiang , Sifan Yang , Yibo Wang , Lijun Zhang

Training in supervised deep learning is computationally demanding, and the convergence behavior is usually not fully understood. We introduce and study a second-order stochastic quasi-Gauss-Newton (SQGN) optimization method that combines…

Machine Learning · Computer Science 2020-07-02 Christopher Thiele , Mauricio Araya-Polo , Detlef Hohl

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

Machine Learning · Statistics 2025-05-20 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

Optimization and Control · Mathematics 2025-11-11 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…

Machine Learning · Computer Science 2022-10-11 Siqi Liang , Yan Sun , Faming Liang

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

Optimization and Control · Mathematics 2025-02-25 Chenhao Yu , Yusu Hong , Junhong Lin

In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…

Optimization and Control · Mathematics 2020-04-16 Darina Dvinskikh , Alexander Tyurin , Alexander Gasnikov , Sergey Omelchenko

In this paper, we introduce a new approach to proving the convergence of the Stochastic Approximation (SA) and the Stochastic Gradient Descent (SGD) algorithms. The new approach is based on a concept called GSLLN (Generalized Strong Law of…

Optimization and Control · Mathematics 2025-11-11 Rajeeva Laxman Karandikar , Bhamidi Visweswara Rao , Mathukumalli Vidyasagar

We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include…

Optimization and Control · Mathematics 2025-01-10 Minh N. Dao , Hung M. Phan , Lindon Roberts

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…

Optimization and Control · Mathematics 2018-09-13 Tao Sun , Yuejiao Sun , Wotao Yin

Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges…

Optimization and Control · Mathematics 2025-03-28 Di Zhang , Suvrajeet Sen

Gradient boosting, a method of building additive ensembles from weak learners, has established itself as a practical and theoretically-motivated approach to approximate functions, especially using decision tree weak learners. Comparable…

Machine Learning · Computer Science 2026-03-26 Abhijit Chowdhary , Elizabeth Newman , Deepanshu Verma

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

Machine Learning · Computer Science 2019-04-08 Craig Wilson , Yuheng Bu , Venugopal Veeravalli

We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each…

Optimization and Control · Mathematics 2024-05-24 Tianshu Wen , Matthew J. Zahr

Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…

Numerical Analysis · Mathematics 2022-01-19 Bangti Jin , Zehui Zhou , Jun Zou

Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…

Machine Learning · Statistics 2020-02-21 Sattar Vakili , Sudeep Salgia , Qing Zhao

In this work we investigate stochastic non-convex optimization problems where the objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such…

Optimization and Control · Mathematics 2021-11-02 Kfir Y. Levy , Ali Kavis , Volkan Cevher

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Optimization and Control · Mathematics 2023-08-15 Da Li , Jingjing Wu , Qingrun Zhang