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By lifting the ReLU function into a higher dimensional space, we develop a smooth multi-convex formulation for training feed-forward deep neural networks (DNNs). This allows us to develop a block coordinate descent (BCD) training algorithm…

Machine Learning · Statistics 2017-11-21 Ziming Zhang , Matthew Brand

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

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Machine Learning · Computer Science 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

A new gradient-based optimization approach by automatically scheduling the learning rate has been proposed recently, which is called Binary Forward Exploration (BFE). The Adaptive version of BFE has also been discussed thereafter. In this…

Machine Learning · Computer Science 2022-09-23 Xin Cao

Continual learning entails learning a sequence of tasks and balancing their knowledge appropriately. With limited access to old training samples, much of the current work in deep neural networks has focused on overcoming catastrophic…

Machine Learning · Computer Science 2023-10-16 Yilin Lyu , Liyuan Wang , Xingxing Zhang , Zicheng Sun , Hang Su , Jun Zhu , Liping Jing

Reinforcement learning (RL) is attracting attention as an effective way to solve sequential optimization problems that involve high dimensional state/action space and stochastic uncertainties. Many such problems involve constraints…

Machine Learning · Computer Science 2021-04-01 Haeun Yoo , Victor M. Zavala , Jay H. Lee

We propose a provably convergent method, called Efficient Learned Descent Algorithm (ELDA), for low-dose CT (LDCT) reconstruction. ELDA is a highly interpretable neural network architecture with learned parameters and meanwhile retains…

Image and Video Processing · Electrical Eng. & Systems 2021-04-28 Qingchao Zhang , Mehrdad Alvandipour , Wenjun Xia , Yi Zhang , Xiaojing Ye , Yunmei Chen

Currently, widely used first-order deep learning optimizers include non-adaptive learning rate optimizers and adaptive learning rate optimizers. The former is represented by SGDM (Stochastic Gradient Descent with Momentum), while the latter…

Machine Learning · Computer Science 2024-09-25 Honglin Qin , Hongye Zheng , Bingxing Wang , Zhizhong Wu , Bingyao Liu , Yuanfang Yang

We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…

Optimization and Control · Mathematics 2022-03-24 Hailiang Liu , Xuping Tian

This paper presents Rudra, a parameter server based distributed computing framework tuned for training large-scale deep neural networks. Using variants of the asynchronous stochastic gradient descent algorithm we study the impact of…

Machine Learning · Statistics 2016-12-07 Suyog Gupta , Wei Zhang , Fei Wang

Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple…

Machine Learning · Computer Science 2017-06-29 Lukas Balles , Javier Romero , Philipp Hennig

We present a novel per-dimension learning rate method for gradient descent called ADADELTA. The method dynamically adapts over time using only first order information and has minimal computational overhead beyond vanilla stochastic gradient…

Machine Learning · Computer Science 2012-12-27 Matthew D. Zeiler

Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…

Machine Learning · Statistics 2018-10-30 Ashok Cutkosky , Robert Busa-Fekete

Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…

Machine Learning · Computer Science 2025-12-23 Ansh Nagwekar

Training deep neural networks with Stochastic Gradient Descent, or its variants, requires careful choice of both learning rate and batch size. While smaller batch sizes generally converge in fewer training epochs, larger batch sizes offer…

Machine Learning · Computer Science 2018-02-15 Aditya Devarakonda , Maxim Naumov , Michael Garland

Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…

Optimization and Control · Mathematics 2021-11-11 Theodoros Mamalis , Dusan Stipanovic , Petros Voulgaris

We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of…

Machine Learning · Computer Science 2016-04-05 Changkyu Song , Sejong Yoon , Vladimir Pavlovic

Aiming at solving large-scale learning problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the learning problem as a consensus problem, the ADMM can…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-05-04 Tsung-Hui Chang , Mingyi Hong , Wei-Cheng Liao , Xiangfeng Wang

The learning rate (LR) schedule is one of the most important hyper-parameters needing careful tuning in training DNNs. However, it is also one of the least automated parts of machine learning systems and usually costs significant manual…

Machine Learning · Computer Science 2021-05-25 Yuchen Jin , Tianyi Zhou , Liangyu Zhao , Yibo Zhu , Chuanxiong Guo , Marco Canini , Arvind Krishnamurthy

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

Optimization and Control · Mathematics 2021-07-07 Junxiang Wang , Fuxun Yu , Xiang Chen , Liang Zhao
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