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We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…

Machine Learning · Statistics 2018-02-14 Adrian Wills , Thomas Schön

Synchronous strategies with data parallelism, such as the Synchronous StochasticGradient Descent (S-SGD) and the model averaging methods, are widely utilizedin distributed training of Deep Neural Networks (DNNs), largely owing to itseasy…

Machine Learning · Computer Science 2022-11-04 Qing Ye , Yuhao Zhou , Mingjia Shi , Yanan Sun , Jiancheng Lv

The local gradient points to the direction of the steepest slope in an infinitesimal neighborhood. An optimizer guided by the local gradient is often trapped in local optima when the loss landscape is multi-modal. A directional Gaussian…

Machine Learning · Computer Science 2020-11-05 Hoang Tran , Guannan Zhang

In recent years, deep neural networks have had great success in machine learning and pattern recognition. Architecture size for a neural network contributes significantly to the success of any neural network. In this study, we optimize the…

Machine Learning · Computer Science 2021-01-19 Yigit Alparslan , Ethan Jacob Moyer , Isamu Mclean Isozaki , Daniel Schwartz , Adam Dunlop , Shesh Dave , Edward Kim

The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…

Machine Learning · Computer Science 2024-06-17 Matthias König , Xiyue Zhang , Holger H. Hoos , Marta Kwiatkowska , Jan N. van Rijn

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

Optimization and Control · Mathematics 2022-12-14 Thang Tran Ngoc , Hai Trinh Ngoc

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

Differentially private (stochastic) gradient descent is the workhorse of DP private machine learning in both the convex and non-convex settings. Without privacy constraints, second-order methods, like Newton's method, converge faster than…

Machine Learning · Computer Science 2023-05-23 Arun Ganesh , Mahdi Haghifam , Thomas Steinke , Abhradeep Thakurta

Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation. This fixed approach is inefficient because of a dynamic trade-off between cost and speed -- larger batches are more…

Machine Learning · Computer Science 2024-10-15 Masaki Adachi , Satoshi Hayakawa , Martin Jørgensen , Xingchen Wan , Vu Nguyen , Harald Oberhauser , Michael A. Osborne

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

In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational…

Numerical Analysis · Mathematics 2021-10-12 Christian Beck , Sebastian Becker , Patrick Cheridito , Arnulf Jentzen , Ariel Neufeld

We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism,…

Optimization and Control · Mathematics 2025-05-08 Kang Liu , Wei Peng , Jianchen Hu

Recent progress on deep learning relies heavily on the quality and efficiency of training algorithms. In this paper, we develop a fast training method motivated by the nonlinear Conjugate Gradient (CG) framework. We propose the Conjugate…

Machine Learning · Computer Science 2021-07-28 Zhiyong Hao , Yixuan Jiang , Huihua Yu , Hsiao-Dong Chiang

The standard L-BFGS method relies on gradient approximations that are not dominated by noise, so that search directions are descent directions, the line search is reliable, and quasi-Newton updating yields useful quadratic models of the…

Optimization and Control · Mathematics 2018-05-31 Raghu Bollapragada , Dheevatsa Mudigere , Jorge Nocedal , Hao-Jun Michael Shi , Ping Tak Peter Tang

Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce a self-adaptive algorithm: the adaptive network enhancement (ANE) method,…

Numerical Analysis · Mathematics 2022-03-02 Zhiqiang Cai , Jingshuang Chen , Min Liu

Problem of finding 2D paths of special shape, e.g. paths comprised of line segments having the property that the angle between any two consecutive segments does not exceed the predefined threshold, is considered in the paper. This problem…

Artificial Intelligence · Computer Science 2018-11-05 Anton Andreychuk , Natalia Soboleva , Konstantin Yakovlev

This paper addresses 3D shape recognition. Recent work typically represents a 3D shape as a set of binary variables corresponding to 3D voxels of a uniform 3D grid centered on the shape, and resorts to deep convolutional neural…

Computer Vision and Pattern Recognition · Computer Science 2016-12-15 Xu Xu , Sinisa Todorovic

This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…

Optimization and Control · Mathematics 2024-02-12 Zhong Zheng , Shiqian Ma , Lingzhou Xue

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Machine Learning · Computer Science 2024-10-28 Shudian Zhao , Jan Kronqvist

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…

Signal Processing · Electrical Eng. & Systems 2020-07-10 Zhan Gao , Alec Koppel , Alejandro Ribeiro