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For distributed computing with Byzantine machines under Privacy Protection (PP) constraints, this paper develops a robust PP distributed quasi-Newton estimation, which only requires the node machines to transmit five vectors to the central…

Machine Learning · Statistics 2024-08-23 Chuhan Wang , Lixing Zhu , Xuehu Zhu

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…

Optimization and Control · Mathematics 2023-03-22 Jiaojiao Zhang , Huikang Liu , Anthony Man-Cho So , Qing Ling

In this paper, we consider a strongly convex finite-sum minimization problem over a decentralized network and propose a communication-efficient decentralized Newton's method for solving it. We first apply dynamic average consensus (DAC) so…

Optimization and Control · Mathematics 2022-10-04 Huikang Liu , Jiaojiao Zhang , Anthony Man-Cho So , Qing Ling

We consider a standard distributed consensus optimization problem where a set of agents connected over an undirected network minimize the sum of their individual local strongly convex costs. Alternating Direction Method of Multipliers ADMM…

Optimization and Control · Mathematics 2022-04-07 Dusan Jakovetic , Natasa Krejic , Natasa Krklec Jerinkic

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

Optimization and Control · Mathematics 2018-05-29 Ching-pei Lee , Cong Han Lim , Stephen J. Wright

In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs,…

Machine Learning · Computer Science 2022-05-30 Nima Dehmamy , Csaba Both , Jianzhi Long , Rose Yu

We consider distributed optimization in random networks where N nodes cooperatively minimize the sum \sum_{i=1}^N f_i(x) of their individual convex costs. Existing literature proposes distributed gradient-like methods that are…

Information Theory · Computer Science 2023-07-19 Dusan Jakovetic , Joao Xavier , Jose M. F. Moura

Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive…

Machine Learning · Computer Science 2018-06-21 Celestine Dünner , Aurelien Lucchi , Matilde Gargiani , An Bian , Thomas Hofmann , Martin Jaggi

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…

Systems and Control · Electrical Eng. & Systems 2019-09-04 Adrian Wills , Thomas Schön

Quasi-Newton (QN) methods provide an efficient alternative to second-order methods for minimizing smooth unconstrained problems. While QN methods generally compose a Hessian estimate based on one secant interpolation per iteration,…

Optimization and Control · Mathematics 2025-04-11 Mokhwa Lee , Yifan Sun

Training deep neural network is a high dimensional and a highly non-convex optimization problem. Stochastic gradient descent (SGD) algorithm and it's variations are the current state-of-the-art solvers for this task. However, due to…

Machine Learning · Computer Science 2017-01-17 Xi He , Dheevatsa Mudigere , Mikhail Smelyanskiy , Martin Takáč

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…

Optimization and Control · Mathematics 2026-04-01 John Chiang

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

We present a novel communication-efficient Newton-type algorithm for finite-sum optimization over a distributed computing environment. Our method, named DINO, overcomes both theoretical and practical shortcomings of similar existing…

Optimization and Control · Mathematics 2020-06-09 Rixon Crane , Fred Roosta

There is growing interest in applying distributed machine learning to edge computing, forming federated edge learning. Federated edge learning faces non-i.i.d. and heterogeneous data, and the communication between edge workers, possibly…

Machine Learning · Computer Science 2022-01-27 Canh T. Dinh , Nguyen H. Tran , Tuan Dung Nguyen , Wei Bao , Amir Rezaei Balef , Bing B. Zhou , Albert Y. Zomaya

Newton's Method is widely used to find the solution of complex non-linear simulation problems in Computer Graphics. To guarantee a descent direction, it is common practice to clamp the negative eigenvalues of each element Hessian prior to…

Graphics · Computer Science 2026-05-26 José Antonio Fernández-Fernández , Fabian Löschner , Jan Bender

Second-order methods for neural network optimization have several advantages over methods based on first-order gradient descent, including better scaling to large mini-batch sizes and fewer updates needed for convergence. But they are…

Machine Learning · Computer Science 2017-12-21 Huishuai Zhang , Caiming Xiong , James Bradbury , Richard Socher

Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…

Optimization and Control · Mathematics 2022-02-01 Dinesh Singh , Hardik Tankaria , Makoto Yamada

This paper considers distributed optimization problems, where each agent cooperatively minimizes the sum of local objective functions through the communication with its neighbors. The widely adopted distributed gradient method in solving…

Optimization and Control · Mathematics 2025-08-19 Yeming Xu , Ziyuan Guo , Kaihong Lu , Huanshui Zhang

The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…

Optimization and Control · Mathematics 2019-01-09 Fatemeh Mansoori , Ermin Wei