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We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…

Statistics Theory · Mathematics 2022-03-03 Bernard Bercu , Jérémie Bigot , Sébastien Gadat , Emilia Siviero

We study a standard distributed optimization framework where $N$ networked nodes collaboratively minimize the sum of their local convex costs. The main body of existing work considers the described problem when the underling network is…

Optimization and Control · Mathematics 2018-03-22 Anit Kumar Sahu , Dusan Jakovetic , Dragana Bajovic , Soummya Kar

Quasi-Newton methods are widely used for solving convex optimization problems due to their ease of implementation, practical efficiency, and strong local convergence guarantees. However, their global convergence is typically established…

Optimization and Control · Mathematics 2025-08-28 Artem Agafonov , Vladislav Ryspayev , Samuel Horváth , Alexander Gasnikov , Martin Takáč , Slavomir Hanzely

We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…

Machine Learning · Computer Science 2019-02-06 Tianyang Li , Anastasios Kyrillidis , Liu Liu , Constantine Caramanis

Quasi-Newton methods form an important class of methods for solving nonlinear optimization problems. In such methods, first order information is used to approximate the second derivative. The aim is to mimic the fast convergence that can be…

Optimization and Control · Mathematics 2025-02-20 Aban Ansari-Önnestam , Anders Forsgren

Training in supervised deep learning is computationally demanding, and the convergence behavior is usually not fully understood. We introduce and study a second-order stochastic quasi-Gauss-Newton (SQGN) optimization method that combines…

Machine Learning · Computer Science 2020-07-02 Christopher Thiele , Mauricio Araya-Polo , Detlef Hohl

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…

Optimization and Control · Mathematics 2024-06-05 Taisei Miyaishi , Ryota Nozawa , Pierre-Louis Poirion , Akiko Takeda

Decentralized optimization is a promising parallel computation paradigm for large-scale data analytics and machine learning problems defined over a network of nodes. This paper is concerned with decentralized non-convex composite problems…

Optimization and Control · Mathematics 2021-10-05 Ran Xin , Subhro Das , Usman A. Khan , Soummya Kar

In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…

Optimization and Control · Mathematics 2026-04-14 Hao Wu , Liping Wang

Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their…

Optimization and Control · Mathematics 2022-10-17 Christian Kanzow , Theresa Lechner

In decentralized learning, a network of nodes cooperate to minimize an overall objective function that is usually the finite-sum of their local objectives, and incorporates a non-smooth regularization term for the better generalization…

Machine Learning · Computer Science 2022-01-25 Xuanjie Li , Yuedong Xu , Jessie Hui Wang , Xin Wang , John C. S. Lui

We present a distributed quasi-Newton (DQN) method, which enables a group of agents to compute an optimal solution of a separable multi-agent optimization problem locally using an approximation of the curvature of the aggregate objective…

Optimization and Control · Mathematics 2024-09-30 Ola Shorinwa , Mac Schwager

In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In…

Optimization and Control · Mathematics 2018-09-05 Jiang Hu , Bo Jiang , Lin Lin , Zaiwen Wen , Yaxiang Yuan

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

In this thesis, we disentangle the generalized Gauss-Newton and approximate inference for Bayesian deep learning. The generalized Gauss-Newton method is an optimization method that is used in several popular Bayesian deep learning…

Machine Learning · Statistics 2020-07-24 Alexander Immer

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

Optimization and Control · Mathematics 2023-10-04 Xiaoxue Jiang

Stochastic optimization methods have become a class of popular optimization tools in machine learning. Especially, stochastic gradient descent (SGD) has been widely used for machine learning problems such as training neural networks due to…

Optimization and Control · Mathematics 2021-02-26 Qingsong Zhang , Feihu Huang , Cheng Deng , Heng Huang

In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded…

Optimization and Control · Mathematics 2025-07-28 Xiaoxi Jia

The problem of minimizing an objective that can be written as the sum of a set of $n$ smooth and strongly convex functions is considered. The Incremental Quasi-Newton (IQN) method proposed here belongs to the family of stochastic and…

Optimization and Control · Mathematics 2017-03-29 Aryan Mokhtari , Mark Eisen , Alejandro Ribeiro

During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information.…

Optimization and Control · Mathematics 2018-10-03 Adrian Wills , Carl Jidling , Thomas Schon