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Deep learning involves a difficult non-convex optimization problem with a large number of weights between any two adjacent layers of a deep structure. To handle large data sets or complicated networks, distributed training is needed, but…

Optimization in Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order optimization methods, which take into account the second-order derivatives are far less…

Machine Learning · Computer Science 2021-04-09 Fares B. Mehouachi , Chaouki Kasmi

Differentiable programming is revolutionizing computational science by enabling automatic differentiation (AD) of numerical simulations. While first-order gradients are well-established, second-order derivatives (Hessians) for implicit…

Computational Engineering, Finance, and Science · Computer Science 2025-05-20 Tianju Xue

Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…

Machine Learning · Computer Science 2025-02-04 Sheng Fang , Yong-Jin Liu , Wei Yao , Chengming Yu , Jin Zhang

Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…

Optimization and Control · Mathematics 2015-08-05 Thomas Furmston , David Barber

The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality). In this paper, we propose to further reduce the…

Optimization and Control · Mathematics 2017-10-03 Mingrui Liu , Tianbao Yang

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

Machine Learning · Computer Science 2021-11-09 Guan-Horng Liu , Tianrong Chen , Evangelos A. Theodorou

Meta-learning is a promising method to achieve efficient training method towards deep neural net and has been attracting increases interests in recent years. But most of the current methods are still not capable to train complex neuron net…

Machine Learning · Computer Science 2018-09-10 Boyu Chen , Wenlian Lu , Ernest Fokoue

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 Nature Machine Intelligence 4, 367 (2022), Schuetz et al provide a scheme to employ graph neural networks (GNN) as a heuristic to solve a variety of classical, NP-hard combinatorial optimization problems. It describes how the network is…

Disordered Systems and Neural Networks · Physics 2023-01-03 Stefan Boettcher

Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…

Machine Learning · Computer Science 2024-12-17 Naoki Sato , Hideaki Iiduka

Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…

Machine Learning · Computer Science 2022-06-07 Daouda Sow , Kaiyi Ji , Yingbin Liang

Second-order training methods have better convergence properties than gradient descent but are rarely used in practice for large-scale training due to their computational overhead. This can be viewed as a hardware limitation (imposed by…

Machine Learning · Computer Science 2024-05-24 Kaelan Donatella , Samuel Duffield , Maxwell Aifer , Denis Melanson , Gavin Crooks , Patrick J. Coles

We develop and analyze several different second-order algorithms for computing a near-optimal solution path of a convex parametric optimization problem with smooth Hessian. Our algorithms are inspired by a differential equation perspective…

Optimization and Control · Mathematics 2023-06-16 Heyuan Liu , Paul Grigas

Optimizing a neural network's performance is a tedious and time taking process, this iterative process does not have any defined solution which can work for all the problems. Optimization can be roughly categorized into - Architecture and…

Machine Learning · Computer Science 2019-12-16 Siddhartha Dhar Choudhury , Shashank Pandey , Kunal Mehrotra

Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…

Machine Learning · Computer Science 2020-11-11 Frithjof Gressmann , Zach Eaton-Rosen , Carlo Luschi

First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…

Machine Learning · Computer Science 2020-02-05 Chih-Hao Fang , Sudhir B Kylasa , Fred Roosta , Michael W. Mahoney , Ananth Grama

Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…

Machine Learning · Computer Science 2017-06-13 Kaifeng Lv , Shunhua Jiang , Jian Li

First-order methods like stochastic gradient descent(SGD) are recently the popular optimization method to train deep neural networks (DNNs), but second-order methods are scarcely used because of the overpriced computing cost in getting the…

Machine Learning · Computer Science 2021-04-01 Jingcheng Zhou , Wei Wei , Zhiming Zheng

Incorporating second order curvature information in gradient based methods have shown to improve convergence drastically despite its computational intensity. In this paper, we propose a stochastic (online) quasi-Newton method with…

Machine Learning · Computer Science 2020-10-16 S. Indrapriyadarsini , Shahrzad Mahboubi , Hiroshi Ninomiya , Hideki Asai