Related papers: A Decentralized Quasi-Newton Method for Dual Formu…

In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating formulas from a certain subclass of the Broyden family. In particular, this subclass includes the well-known DFP, BFGS and SR1 updates. However,…

Stochastic gradient descent and other first-order variants, such as Adam and AdaGrad, are commonly used in the field of deep learning due to their computational efficiency and low-storage memory requirements. However, these methods do not…

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional…

Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian…

In this paper, a class of Decentralized Approximate Newton (DEAN) methods for addressing convex optimization on a networked system are developed, where nodes in the networked system seek for a consensus that minimizes the sum of their…

In this paper, we explore the non-asymptotic global convergence rates of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method implemented with exact line search. Notably, due to Dixon's equivalence result, our findings are also applicable to…

This paper considers decentralized consensus optimization problems where different summands of a global objective function are available at nodes of a network that can communicate with neighbors only. The proximal method of multipliers is…

To address the communication burden and privacy concerns associated with the centralized server in Federated Learning (FL), Decentralized Federated Learning (DFL) has emerged, which discards the server with a peer-to-peer (P2P)…

Federated learning (FL) is a promising technology that enables edge devices/clients to collaboratively and iteratively train a machine learning model under the coordination of a central server. The most common approach to FL is first-order…

The classical convergence analysis of quasi-Newton methods assumes that the function and gradients employed at each iteration are exact. In this paper, we consider the case when there are (bounded) errors in both computations and establish…

In this paper, based on function information, we propose a modified BFGS-type method for nonconvex multiobjective optimization problems (MFQNMO). In the multiobjective quasi-Newton method (QNMO), each iteration involves separately…

RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is…

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…

To mitigate the privacy leakages and communication burdens of Federated Learning (FL), decentralized FL (DFL) discards the central server and each client only communicates with its neighbors in a decentralized communication network.…

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…

Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised…

In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmannians or a product of Grassmannians. Specifically we defined BFGS and L-BFGS updates in local and global coordinates…

We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or…

We analyze the convergence of decentralized consensus algorithm with delayed gradient information across the network. The nodes in the network privately hold parts of the objective function and collaboratively solve for the consensus…

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…