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Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…

Machine Learning · Computer Science 2020-06-16 Yunwen Lei , Yiming Ying

We study the generalization properties of the popular stochastic optimization method known as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the…

Machine Learning · Computer Science 2021-08-17 Gergely Neu , Gintare Karolina Dziugaite , Mahdi Haghifam , Daniel M. Roy

Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms.…

Machine Learning · Computer Science 2023-05-30 Mingze Wang , Chao Ma

Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…

Machine Learning · Computer Science 2020-06-15 Raef Bassily , Vitaly Feldman , Cristóbal Guzmán , Kunal Talwar

Many machine learning tasks can be formulated as Regularized Empirical Risk Minimization (R-ERM), and solved by optimization algorithms such as gradient descent (GD), stochastic gradient descent (SGD), and stochastic variance reduction…

Machine Learning · Statistics 2016-09-28 Qi Meng , Yue Wang , Wei Chen , Taifeng Wang , Zhi-Ming Ma , Tie-Yan Liu

We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for…

Machine Learning · Computer Science 2018-02-19 Ilja Kuzborskij , Christoph H. Lampert

Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a…

Machine Learning · Computer Science 2021-02-11 Yikai Zhang , Wenjia Zhang , Sammy Bald , Vamsi Pingali , Chao Chen , Mayank Goswami

Stochastic Gradient Descent (SGD) is a widely deployed optimization procedure throughout data-driven and simulation-driven disciplines, which has drawn a substantial interest in understanding its global behavior across a broad class of…

Optimization and Control · Mathematics 2021-04-02 Vivak Patel , Shushu Zhang

Stochastic Gradient Descent (SGD) is fundamental for training deep neural networks, especially in non-convex settings. Understanding SGD's generalization properties is crucial for ensuring robust model performance on unseen data. In this…

Machine Learning · Statistics 2025-06-24 Wenjun Xiong , Juan Ding , Xinlei Zuo , Qizhai Li

Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…

Machine Learning · Computer Science 2019-12-16 Yunwen Lei , Ting Hu , Guiying Li , Ke Tang

We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…

Machine Learning · Computer Science 2023-01-13 Tomer Koren , Roi Livni , Yishay Mansour , Uri Sherman

We provide sharp path-dependent generalization and excess risk guarantees for the full-batch Gradient Descent (GD) algorithm on smooth losses (possibly non-Lipschitz, possibly nonconvex). At the heart of our analysis is an upper bound on…

Machine Learning · Statistics 2023-02-13 Konstantinos E. Nikolakakis , Farzin Haddadpour , Amin Karbasi , Dionysios S. Kalogerias

This paper presents a new generalization error analysis for Decentralized Stochastic Gradient Descent (D-SGD) based on algorithmic stability. The obtained results overhaul a series of recent works that suggested an increased instability due…

Machine Learning · Computer Science 2024-06-14 Batiste Le Bars , Aurélien Bellet , Marc Tommasi , Kevin Scaman , Giovanni Neglia

This work studies the generalization error of gradient methods. More specifically, we focus on how training steps $T$ and step-size $\eta$ might affect generalization in smooth stochastic convex optimization (SCO) problems. We first provide…

Machine Learning · Computer Science 2023-05-11 Peiyuan Zhang , Jiaye Teng , Jingzhao Zhang

The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent…

Machine Learning · Statistics 2021-02-24 Tao Sun , Dongsheng Li , Bao Wang

Decentralized stochastic gradient descent (D-SGD) is an efficient method for large-scale distributed learning. Existing generalization studies mainly address expected results, achieving rates limited to $\mathcal{O}\left(\frac{1}{\delta…

Machine Learning · Computer Science 2026-05-12 Jiahuan Wang , Ping Luo , Ziqing Wen , Dongsheng Li , Tao Sun

We give a new separation result between the generalization performance of stochastic gradient descent (SGD) and of full-batch gradient descent (GD) in the fundamental stochastic convex optimization model. While for SGD it is well-known that…

Machine Learning · Computer Science 2021-07-01 Idan Amir , Tomer Koren , Roi Livni

Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…

Machine Learning · Computer Science 2022-11-03 Dragana Bajovic , Dusan Jakovetic , Soummya Kar

This paper studies the generalization performance of iterates obtained by Gradient Descent (GD), Stochastic Gradient Descent (SGD) and their proximal variants in high-dimensional robust regression problems. The number of features is…

Statistics Theory · Mathematics 2024-11-05 Kai Tan , Pierre C. Bellec

Stochastic Gradient Descent (SGD) plays a central role in modern machine learning. While there is extensive work on providing error upper bound for SGD, not much is known about SGD error lower bound. In this paper, we study the convergence…

Optimization and Control · Mathematics 2019-10-21 Zhiyan Ding , Yiding Chen , Qin Li , Xiaojin Zhu
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