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Federated learning is an efficient machine learning tool for dealing with heterogeneous big data and privacy protection. Federated learning methods with regularization can control the level of communications between the central and local…

Machine Learning · Computer Science 2024-11-05 Langming Liu , Dingxuan Zhou

The theory underlying robust distributed learning algorithms, designed to resist adversarial machines, matches empirical observations when data is homogeneous. Under data heterogeneity however, which is the norm in practical scenarios,…

Machine Learning · Computer Science 2023-10-31 Youssef Allouah , Rachid Guerraoui , Nirupam Gupta , Rafaël Pinot , Geovani Rizk

Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to…

Optimization and Control · Mathematics 2017-10-24 Sindri Magnusson , Chinwendu Enyioha , Na Li , Carlo Fischione , Vahid Tarokh

Neural networks have revolutionized various domains, exhibiting remarkable accuracy in tasks like natural language processing and computer vision. However, their vulnerability to slight alterations in input samples poses challenges,…

Computer Vision and Pattern Recognition · Computer Science 2023-11-15 Shashank Kotyan , Danilo Vasconcellos Vargas

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

We study the learning performance of gradient descent when the empirical risk is weakly convex, namely, the smallest negative eigenvalue of the empirical risk's Hessian is bounded in magnitude. By showing that this eigenvalue can control…

Machine Learning · Statistics 2021-06-02 Dominic Richards , Mike Rabbat

This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative…

Optimization and Control · Mathematics 2025-07-02 Pierre Vernimmen , François Glineur

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we…

Machine Learning · Statistics 2023-06-02 Dongyoon Yang , Insung Kong , Yongdai Kim

We consider a convex unconstrained optimization problem that arises in a network of agents whose goal is to cooperatively optimize the sum of the individual agent objective functions through local computations and communications. For this…

Optimization and Control · Mathematics 2008-03-11 Angelia Nedić , Alex Olshevsky , Asuman Ozdaglar , John N. Tsitsiklis

Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…

Machine Learning · Computer Science 2024-01-11 Liang Zhang , Junchi Yang , Amin Karbasi , Niao He

We consider offline Imitation Learning from corrupted demonstrations where a constant fraction of data can be noise or even arbitrary outliers. Classical approaches such as Behavior Cloning assumes that demonstrations are collected by an…

Machine Learning · Computer Science 2022-02-01 Liu Liu , Ziyang Tang , Lanqing Li , Dijun Luo

Conventional sampling techniques fall short of drawing descriptive sketches of the data when the data is grossly corrupted as such corruptions break the low rank structure required for them to perform satisfactorily. In this paper, we…

Machine Learning · Computer Science 2016-11-21 Mostafa Rahmani , George Atia

An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…

Optimization and Control · Mathematics 2018-06-27 Frank E. Curtis , Katya Scheinberg , Rui Shi

Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp functions that are only weakly convex, provided that the subgradient methods are…

Optimization and Control · Mathematics 2018-03-08 Damek Davis , Dmitriy Drusvyatskiy , Kellie J. MacPhee , Courtney Paquette

This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…

Optimization and Control · Mathematics 2024-11-07 Wenzhi Gao , Qi Deng

Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…

Machine Learning · Computer Science 2022-12-21 Jongheon Jeong , Seojin Kim , Jinwoo Shin

We study the convergence of the last iterate in subgradient methods applied to the minimization of a nonsmooth convex function with bounded subgradients. We first introduce a proof technique that generalizes the standard analysis of…

Optimization and Control · Mathematics 2023-07-24 Moslem Zamani , François Glineur

We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint…

Machine Learning · Statistics 2015-04-02 Junhong Lin , Lorenzo Rosasco , Ding-Xuan Zhou

Data-driven models, especially deep learning classifiers often demonstrate great success on clean datasets. Yet, they remain vulnerable to common data distortions such as adversarial and common corruption perturbations. These perturbations…

We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…

Optimization and Control · Mathematics 2018-09-27 Mostafa Amini , Farzad Yousefian