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In machine learning and neural network optimization, algorithms like incremental gradient, and shuffle SGD are popular due to minimizing the number of cache misses and good practical convergence behavior. However, their optimization…

Machine Learning · Computer Science 2024-02-13 Anastasia Koloskova , Nikita Doikov , Sebastian U. Stich , Martin Jaggi

Two new stochastic variance-reduced algorithms named SARAH and SPIDER have been recently proposed, and SPIDER has been shown to achieve a near-optimal gradient oracle complexity for nonconvex optimization. However, the theoretical advantage…

Optimization and Control · Mathematics 2019-05-17 Yi Zhou , Zhe Wang , Kaiyi Ji , Yingbin Liang , Vahid Tarokh

Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…

Optimization and Control · Mathematics 2023-06-27 Ziyi Chen , Yi Zhou , Yingbin Liang , Zhaosong Lu

$L_0$-smoothness, which has been pivotal to advancing decentralized optimization theory, is often fairly restrictive for modern tasks like deep learning. The recent advent of relaxed $(L_0,L_1)$-smoothness condition enables improved…

Optimization and Control · Mathematics 2025-08-13 Zhanhong Jiang , Aditya Balu , Soumik Sarkar

We study nonlinearly preconditioned gradient methods for smooth nonconvex optimization problems, focusing on sigmoid preconditioners that inherently perform a form of gradient clipping akin to the widely used gradient clipping technique.…

Optimization and Control · Mathematics 2025-10-14 Konstantinos Oikonomidis , Jan Quan , Panagiotis Patrinos

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

Optimization and Control · Mathematics 2018-05-01 James V. Burke , Frank E. Curtis , Adrian S. Lewis , Michael L. Overton , Lucas E. A. Simões

Previous research has shown that constraining the gradient of loss function with respect to model-predicted probabilities can enhance the model robustness against noisy labels. These methods typically specify a fixed optimal threshold for…

Machine Learning · Computer Science 2024-12-24 Xichen Ye , Yifan Wu , Weizhong Zhang , Xiaoqiang Li , Yifan Chen , Cheng Jin

Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate…

Machine Learning · Computer Science 2021-03-19 Xiangyi Chen , Zhiwei Steven Wu , Mingyi Hong

Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is…

Machine Learning · Computer Science 2021-07-30 Zeyuan Allen-Zhu

The learning rate is perhaps the single most important parameter in the training of neural networks and, more broadly, in stochastic (nonconvex) optimization. Accordingly, there are numerous effective, but poorly understood, techniques for…

Machine Learning · Computer Science 2020-04-16 Bin Shi , Weijie J. Su , Michael I. Jordan

In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability…

Optimization and Control · Mathematics 2020-10-26 Eduard Gorbunov , Marina Danilova , Alexander Gasnikov

Motivated by understanding and analysis of large-scale machine learning under heavy-tailed gradient noise, we study decentralized optimization with gradient clipping, i.e., in which certain clipping operators are applied to the gradients or…

Optimization and Control · Mathematics 2024-11-12 Shuhua Yu , Dusan Jakovetic , Soummya Kar

We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…

Optimization and Control · Mathematics 2016-08-26 Zeyuan Allen-Zhu , Elad Hazan

Motivated by the increasing popularity and importance of large-scale training under differential privacy (DP) constraints, we study distributed gradient methods with gradient clipping, i.e., clipping applied to the gradients computed from…

Machine Learning · Computer Science 2023-05-31 Sarit Khirirat , Eduard Gorbunov , Samuel Horváth , Rustem Islamov , Fakhri Karray , Peter Richtárik

Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can…

Machine Learning · Computer Science 2025-11-05 Yuheng Zhao , Yu-Hu Yan , Kfir Yehuda Levy , Peng Zhao

Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…

Optimization and Control · Mathematics 2025-06-09 Ruichen Jiang , Devyani Maladkar , Aryan Mokhtari

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Optimization and Control · Mathematics 2024-03-08 David Newton , Raghu Bollapragada , Raghu Pasupathy , Nung Kwan Yip

In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed…

Machine Learning · Statistics 2017-02-07 Aleksandr Aravkin , Damek Davis

Modern machine learning is dominated by complex, overparameterized architectures capable of interpolating data and achieving zero training loss. For such models, we investigate the convergence properties of two popular modifications to…

Optimization and Control · Mathematics 2026-05-27 Aleksandr Lobanov , Anastasia Koloskova

We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…

Optimization and Control · Mathematics 2025-12-24 Zepeng Wang , Juan Peypouquet