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One classical canon of statistics is that large models are prone to overfitting, and model selection procedures are necessary for high dimensional data. However, many overparameterized models, such as neural networks, perform very well in…

Machine Learning · Statistics 2021-01-05 Xi Chen , Qiang Liu , Xin T. Tong

Learning rate schedule can significantly affect generalization performance in modern neural networks, but the reasons for this are not yet understood. Li-Wei-Ma (2019) recently proved this behavior can exist in a simplified non-convex…

Machine Learning · Computer Science 2020-05-18 Preetum Nakkiran

In this paper, we study large-scale convex optimization algorithms based on the Newton method applied to regularized generalized self-concordant losses, which include logistic regression and softmax regression. We first prove that our new…

Optimization and Control · Mathematics 2019-11-22 Ulysse Marteau-Ferey , Francis Bach , Alessandro Rudi

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…

Machine Learning · Statistics 2022-06-09 Xiao-Tong Yuan , Ping Li

Generalization is a central problem in Machine Learning. Most prediction methods require careful calibration of hyperparameters carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of this paper is…

Machine Learning · Computer Science 2020-06-15 Karim Lounici , Katia Meziani , Benjamin Riu

We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…

Machine Learning · Computer Science 2020-06-23 Ben London

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

Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…

Machine Learning · Computer Science 2019-03-19 Vitaly Feldman , Jan Vondrak

We develop generalization error bounds for stochastic gradient descent (SGD) with label noise in non-convex settings under uniform dissipativity and smoothness conditions. Under a suitable choice of semimetric, we establish a contraction in…

Machine Learning · Statistics 2023-11-02 Jung Eun Huh , Patrick Rebeschini

In this paper we study the problem of convergence and generalization error bound of stochastic momentum for deep learning from the perspective of regularization. To do so, we first interpret momentum as solving an $\ell_2$-regularized…

Machine Learning · Computer Science 2019-06-04 Ziming Zhang , Wenju Xu , Alan Sullivan

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…

Optimization and Control · Mathematics 2023-01-19 X. Y. Han , Adrian S. Lewis

We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…

Machine Learning · Computer Science 2021-06-22 Benedict Leimkuhler , Timothée Pouchon , Tiffany Vlaar , Amos Storkey

Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…

Machine Learning · Computer Science 2021-02-22 Andreas Maurer , Daniela A. Parletta , Andrea Paudice , Massimiliano Pontil

This paper presents a novel information-theoretic perspective on generalization in machine learning by framing the learning problem within the context of lossy compression and applying finite blocklength analysis. In our approach, the…

Machine Learning · Computer Science 2026-02-05 Kosuke Sugiyama , Masato Uchida

We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…

Machine Learning · Computer Science 2018-09-20 Dominic Richards , Patrick Rebeschini

Understanding generalization in overparameterized neural networks hinges on the interplay between the data geometry, neural architecture, and training dynamics. In this paper, we theoretically explore how data geometry controls this…

Machine Learning · Statistics 2026-05-08 Tongtong Liang , Alexander Cloninger , Rahul Parhi , Yu-Xiang Wang

Self-training is a classical approach in semi-supervised learning which is successfully applied to a variety of machine learning problems. Self-training algorithm generates pseudo-labels for the unlabeled examples and progressively refines…

Machine Learning · Computer Science 2020-06-22 Samet Oymak , Talha Cihad Gulcu

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…

Optimization and Control · Mathematics 2024-07-11 Yuya Yamakawa , Nobuo Yamashita

This paper analyzes the contraction of the primal-dual gradient optimization via contraction theory in the context of discrete-time updating dynamics. The contraction theory based on Riemannian manifolds is first established for convergence…

Optimization and Control · Mathematics 2019-07-25 Yanxu Su , Yang Shi , Changyin Sun

Pairwise learning includes various machine learning tasks, with ranking and metric learning serving as the primary representatives. While randomized coordinate descent (RCD) is popular in various learning problems, there is much less…

Machine Learning · Computer Science 2025-03-04 Liang Wu , Ruixi Hu , Yunwen Lei