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Neural network compression techniques have become increasingly popular as they can drastically reduce the storage and computation requirements for very large networks. Recent empirical studies have illustrated that even simple pruning…

Machine Learning · Statistics 2021-06-08 Melih Barsbey , Milad Sefidgaran , Murat A. Erdogdu , Gaël Richard , Umut Şimşekli

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

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

Machine Learning · Statistics 2020-06-12 Liam Hodgkinson , Michael W. Mahoney

While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new…

Machine Learning · Computer Science 2019-07-26 Xinyan Li , Qilong Gu , Yingxue Zhou , Tiancong Chen , Arindam Banerjee

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

Machine Learning · Computer Science 2022-10-11 Vivak Patel , Shushu Zhang , Bowen Tian

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

Since the celebrated works of Russo and Zou (2016,2019) and Xu and Raginsky (2017), it has been well known that the generalization error of supervised learning algorithms can be bounded in terms of the mutual information between their input…

Machine Learning · Statistics 2022-07-20 Gábor Lugosi , Gergely Neu

There is an increasing realization that algorithmic inductive biases are central in preventing overfitting; empirically, we often see a benign overfitting phenomenon in overparameterized settings for natural learning algorithms, such as…

Machine Learning · Computer Science 2021-10-14 Difan Zou , Jingfeng Wu , Vladimir Braverman , Quanquan Gu , Sham M. Kakade

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

In the era of large-scale neural network models, optimization algorithms often struggle with generalization due to an overreliance on training loss. One key insight widely accepted in the machine learning community is the idea that wide…

Machine Learning · Computer Science 2025-09-01 Bodu Gong , Gustavo Enrique Batista , Pierre Lafaye de Micheaux

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

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…

Machine Learning · Computer Science 2024-01-24 Gregory Dexter , Borja Ocejo , Sathiya Keerthi , Aman Gupta , Ayan Acharya , Rajiv Khanna

This paper studies the generalization bounds for the empirical saddle point (ESP) solution to stochastic saddle point (SSP) problems. For SSP with Lipschitz continuous and strongly convex-strongly concave objective functions, we establish…

Optimization and Control · Mathematics 2020-06-04 Junyu Zhang , Mingyi Hong , Mengdi Wang , Shuzhong Zhang

Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper,…

Machine Learning · Computer Science 2018-05-22 Yi Xu , Shenghuo Zhu , Sen Yang , Chi Zhang , Rong Jin , Tianbao Yang

Algorithm-dependent generalization error bounds are central to statistical learning theory. A learning algorithm may use a large hypothesis space, but the limited number of iterations controls its model capacity and generalization error.…

Machine Learning · Computer Science 2017-07-20 Wenlong Mou , Liwei Wang , Xiyu Zhai , Kai Zheng

This paper studies a risk minimization problem with decision dependent data distribution. The problem pertains to the performative prediction setting in which a trained model can affect the outcome estimated by the model. Such dependency…

Optimization and Control · Mathematics 2025-01-07 Qiang Li , Hoi-To Wai

We establish novel generalization bounds for learning algorithms that converge to global minima. We do so by deriving black-box stability results that only depend on the convergence of a learning algorithm and the geometry around the…

Machine Learning · Statistics 2017-10-25 Zachary Charles , Dimitris Papailiopoulos

Stochastic gradient descent with momentum (SGDM) is one of the most widely used optimization algorithms in machine learning. While optimization properties of SGDM have been extensively studied in the literature, it remains insufficiently…

Machine Learning · Computer Science 2026-05-28 Yunwen Lei , Zimeng Wang , Xiaoming Yuan

Recent empirical evidence indicates that many machine learning applications involve heavy-tailed gradient noise, which challenges the standard assumptions of bounded variance in stochastic optimization. Gradient clipping has emerged as a…

Optimization and Control · Mathematics 2025-07-10 Florian Hübler , Ilyas Fatkhullin , Niao He

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