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Optimizing deep neural networks is largely thought to be an empirical process, requiring manual tuning of several hyper-parameters, such as learning rate, weight decay, and dropout rate. Arguably, the learning rate is the most important of…

Machine Learning · Computer Science 2020-08-04 Rahul Yedida , Snehanshu Saha , Tejas Prashanth

One of the most critical problems in machine learning is HyperParameter Optimization (HPO), since choice of hyperparameters has a significant impact on final model performance. Although there are many HPO algorithms, they either have no…

Machine Learning · Computer Science 2023-06-09 Yasong Feng , Weijian Luo , Yimin Huang , Tianyu Wang

Effective hyper-parameter tuning is essential to guarantee the performance that neural networks have come to be known for. In this work, a principled approach to choosing the learning rate is proposed for shallow feedforward neural…

Machine Learning · Computer Science 2020-10-01 Thulasi Tholeti , Sheetal Kalyani

Improving adversarial robustness of neural networks remains a major challenge. Fundamentally, training a neural network via gradient descent is a parameter estimation problem. In adaptive control, maintaining persistency of excitation (PoE)…

Machine Learning · Statistics 2021-10-18 Kaustubh Sridhar , Oleg Sokolsky , Insup Lee , James Weimer

We aim to design adaptive online learning algorithms that take advantage of any special structure that might be present in the learning task at hand, with as little manual tuning by the user as possible. A fundamental obstacle that comes up…

Machine Learning · Computer Science 2019-05-31 Zakaria Mhammedi , Wouter M. Koolen , Tim van Erven

Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through…

Machine Learning · Computer Science 2018-06-20 Lisha Li , Kevin Jamieson , Giulia DeSalvo , Afshin Rostamizadeh , Ameet Talwalkar

The choice of learning rate (LR) functions and policies has evolved from a simple fixed LR to the decaying LR and the cyclic LR, aiming to improve the accuracy and reduce the training time of Deep Neural Networks (DNNs). This paper presents…

Machine Learning · Computer Science 2022-10-25 Yanzhao Wu , Ling Liu

In the usual deep neural network optimization process, the learning rate is the most important hyper parameter, which greatly affects the final convergence effect. The purpose of learning rate is to control the stepsize and gradually reduce…

Machine Learning · Computer Science 2019-05-02 Jiakai Wei

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…

Machine Learning · Computer Science 2020-04-21 Fabian Latorre , Paul Rolland , Volkan Cevher

The learning rate is a critical hyperparameter for deep learning tasks since it determines the extent to which the model parameters are updated during the learning course. However, the choice of learning rates typically depends on empirical…

Machine Learning · Computer Science 2024-03-13 Minghan Fu , Fang-Xiang Wu

The performance of a deep neural network is highly dependent on its training, and finding better local optimal solutions is the goal of many optimization algorithms. However, existing optimization algorithms show a preference for descent…

Computer Vision and Pattern Recognition · Computer Science 2019-12-06 Huangxing Lin , Weihong Zeng , Xinghao Ding , Yue Huang , Chenxi Huang , John Paisley

We develop an approach to efficiently grow neural networks, within which parameterization and optimization strategies are designed by considering their effects on the training dynamics. Unlike existing growing methods, which follow simple…

Machine Learning · Computer Science 2023-06-23 Xin Yuan , Pedro Savarese , Michael Maire

Backpropagation with gradient descent is a common optimization strategy employed by most neural network architectures in machine learning. However, finding optimal hyperparameters to guide training has proven challenging. While it is widely…

Machine Learning · Computer Science 2026-05-20 Vy Bui , Hang Yu , Karthik Kantipudi , Ziv Yaniv , Stefan Jaeger

In this paper, we propose BPGrad, a novel approximate algorithm for deep nueral network training, based on adaptive estimates of feasible region via branch-and-bound. The method is based on the assumption of Lipschitz continuity in…

Computer Vision and Pattern Recognition · Computer Science 2021-10-26 Yuanwei Wu , Ziming Zhang , Guanghui Wang

Neural networks are typically trained with a single learning rate across all layers. While recent empirical evidence suggests that assigning layer-specific learning rates can accelerate training, a principled understanding of the conditions…

Machine Learning · Computer Science 2026-05-26 Sihan Zeng , Sujay Bhatt , Sumitra Ganesh

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…

Machine Learning · Statistics 2020-08-11 Henry Gouk , Eibe Frank , Bernhard Pfahringer , Michael J. Cree

We propose multirate training of neural networks: partitioning neural network parameters into "fast" and "slow" parts which are trained on different time scales, where slow parts are updated less frequently. By choosing appropriate…

Machine Learning · Computer Science 2022-11-02 Tiffany Vlaar , Benedict Leimkuhler

Most learning to rank research has assumed that the utility of different documents is independent, which results in learned ranking functions that return redundant results. The few approaches that avoid this have rather unsatisfyingly…

Machine Learning · Computer Science 2012-09-04 Aleksandrs Slivkins , Filip Radlinski , Sreenivas Gollapudi

Training neural networks can be challenging, especially as the complexity of the problem increases. Despite using wider or deeper networks, training them can be a tedious process, especially if a wrong choice of the hyperparameter is made.…

Computational Engineering, Finance, and Science · Computer Science 2025-07-30 D. Veerababu , Ashwin A. Raikar , Prasanta K. Ghosh

Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in the input is the Lipschitz constant of the input-output map…

Machine Learning · Computer Science 2021-04-30 Patricia Pauli , Anne Koch , Julian Berberich , Paul Kohler , Frank Allgöwer
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