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Second-order methods are emerging as promising alternatives to standard first-order optimizers such as gradient descent and ADAM for training neural networks. Though the advantages of including curvature information in computing…

Machine Learning · Computer Science 2025-10-15 Conor Rowan

In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental…

Statistics Theory · Mathematics 2015-05-19 Robert M. Freund , Paul Grigas , Rahul Mazumder

Iterative first-order methods such as gradient descent and its variants are widely used for solving optimization and machine learning problems. There has been recent interest in analytic or numerically efficient methods for computing…

Systems and Control · Computer Science 2020-03-24 Laurent Lessard , Peter Seiler

The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover,…

Numerical Analysis · Mathematics 2025-02-20 Sofya Maslovskaya , Sina Ober-Blöbaum , Christian Offen , Pranav Singh , Boris Wembe

Fine-tuning Large Language Models (LLMs) has proven effective for a variety of downstream tasks. However, as LLMs grow in size, the memory demands for backpropagation become increasingly prohibitive. Zeroth-order (ZO) optimization methods…

Machine Learning · Computer Science 2025-07-25 Ziming Yu , Pan Zhou , Sike Wang , Jia Li , Mi Tian , Hua Huang

Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a…

Optimization and Control · Mathematics 2016-05-23 Dan Garber , Ofer Meshi

We propose a new per-layer adaptive step-size procedure for stochastic first-order optimization methods for minimizing empirical loss functions in deep learning, eliminating the need for the user to tune the learning rate (LR). The proposed…

Machine Learning · Computer Science 2023-07-07 Achraf Bahamou , Donald Goldfarb

Structured pruning is a commonly used convolutional neural network (CNN) compression approach. Pruning rate setting is a fundamental problem in structured pruning. Most existing works introduce too many additional learnable parameters to…

Computer Vision and Pattern Recognition · Computer Science 2023-09-26 Pucheng Zhai , Kailing Guo , Fang Liu , Xiaofen Xing , Xiangmin Xu

We propose proximal backpropagation (ProxProp) as a novel algorithm that takes implicit instead of explicit gradient steps to update the network parameters during neural network training. Our algorithm is motivated by the step size…

Machine Learning · Computer Science 2018-02-21 Thomas Frerix , Thomas Möllenhoff , Michael Moeller , Daniel Cremers

We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by…

Machine Learning · Computer Science 2022-04-29 Yunfei Teng , Wenbo Gao , Francois Chalus , Anna Choromanska , Donald Goldfarb , Adrian Weller

Artificial Intelligence algorithms have been steadily increasing in popularity and usage. Deep Learning, allows neural networks to be trained using huge datasets and also removes the need for human extracted features, as it automates the…

Neural and Evolutionary Computing · Computer Science 2020-05-11 Vasco Lopes , Paulo Fazendeiro

Deep neural networks are typically trained using global error signals that backpropagate (BP) end-to-end, which is not only biologically implausible but also suffers from the update locking problem and requires huge memory consumption.…

Neural and Evolutionary Computing · Computer Science 2024-02-28 Chenxiang Ma , Jibin Wu , Chenyang Si , Kay Chen Tan

In modern deep learning, the models are learned by applying gradient updates using an optimizer, which transforms the updates based on various statistics. Optimizers are often hand-designed and tuning their hyperparameters is a big part of…

Machine Learning · Computer Science 2024-10-08 Gus Kristiansen , Mark Sandler , Andrey Zhmoginov , Nolan Miller , Anirudh Goyal , Jihwan Lee , Max Vladymyrov

This paper tackles the problem of training a deep convolutional neural network of both low-bitwidth weights and activations. Optimizing a low-precision network is very challenging due to the non-differentiability of the quantizer, which may…

Computer Vision and Pattern Recognition · Computer Science 2021-06-07 Bohan Zhuang , Jing Liu , Mingkui Tan , Lingqiao Liu , Ian Reid , Chunhua Shen

Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…

Optimization and Control · Mathematics 2019-11-27 Chin Pang Ho , Michal Kocvara , Panos Parpas

After showing the efficiency of feedforward networks to estimate control in high dimension in the global optimization of some storages problems, we develop a modification of an algorithm based on some dynamic programming principle. We show…

Optimization and Control · Mathematics 2023-05-31 Xavier Warin

We consider distributed optimization as motivated by machine learning in a multi-agent system: each agent holds local data and the goal is to minimize an aggregate loss function over a common model, via an interplay of local training and…

Optimization and Control · Mathematics 2025-04-08 Dingran Yi , Fanhao Zeng , Nikolaos M. Freris

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

Machine Learning · Computer Science 2024-10-16 Yuntian Gu , Xuzheng Chen

Deep neural policies have unlocked agile flight for quadcopters, adaptive grasping for manipulators, and reliable navigation for ground robots, yet their millions of weights conflict with the tight memory and real-time constraints of…

Robotics · Computer Science 2025-07-08 Maksym Shamrai

Model depth is a double-edged sword in deep learning: deeper models achieve higher accuracy but require higher computational cost. To efficiently train models at scale, an effective strategy is the progressive training, which scales up…

Machine Learning · Computer Science 2025-11-10 Zhiqi Bu