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In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…

Machine Learning · Computer Science 2019-05-29 Michał Dereziński , Michael W. Mahoney

We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…

Machine Learning · Computer Science 2014-05-15 Ohad Shamir , Nathan Srebro , Tong Zhang

We propose a new distributed algorithm for computing a truncated Newton method, where the main diagonal of the Hessian is computed using belief propagation. As a case study for this approach, we examine the sensor selection problem, a…

Information Theory · Computer Science 2010-01-14 Danny Bickson , Danny Dolev

In this paper, we propose a distributed second- order method for reinforcement learning. Our approach is the fastest in literature so-far as it outperforms state-of-the-art methods, including ADMM, by significant margins. We achieve this by…

Optimization and Control · Mathematics 2016-08-08 Rasul Tutunov , Haitham Bou-Ammar , Ali Jadbabaie

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a novel Distributed Approx-Newton algorithm that approximates the standard Newton optimization method. A main property of this…

Numerical Analysis · Computer Science 2017-03-24 Tor Anderson , Chin-Yao Chang , Sonia Martinez

Newton's method leverages curvature information to boost performance, and thus outperforms first-order methods for distributed learning problems. However, Newton's method is not practical in large-scale and heterogeneous learning…

Machine Learning · Computer Science 2024-12-18 Shuzhen Chen , Yuan Yuan , Youming Tao , Tianzhu Wang , Zhipeng Cai , Dongxiao Yu

We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…

Optimization and Control · Mathematics 2021-05-21 Hossein Moradian , Solmaz S. Kia

In a multi-agent network, we consider the problem of minimizing an objective function that is expressed as the sum of private convex and smooth functions, and a (possibly) non-differentiable convex regularizer. We propose a novel…

Optimization and Control · Mathematics 2021-09-30 Yichuan Li , Nikolaos M. Freris , Petros Voulgaris , Dusan Stipanovic

We propose and analyze a stochastic Newton algorithm for homogeneous distributed stochastic convex optimization, where each machine can calculate stochastic gradients of the same population objective, as well as stochastic Hessian-vector…

Optimization and Control · Mathematics 2021-10-08 Brian Bullins , Kumar Kshitij Patel , Ohad Shamir , Nathan Srebro , Blake Woodworth

Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative…

Optimization and Control · Mathematics 2015-03-17 Ermin Wei , Asuman Ozdaglar , Ali Jadbabaie

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

Optimization and Control · Mathematics 2016-02-29 Farbod Roosta-Khorasani , Michael W. Mahoney

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…

Optimization and Control · Mathematics 2016-09-06 Haishan Ye , Luo Luo , Zhihua Zhang

Distributed optimization is widely used in large-scale and privacy-preserving machine learning, where each agent stores a local objective and communicates only with its neighbors in a connected network. We study decentralized second-order…

In this paper, we consider distributed algorithms for solving the empirical risk minimization problem under the master/worker communication model. We develop a distributed asynchronous quasi-Newton algorithm that can achieve superlinear…

Optimization and Control · Mathematics 2019-06-11 Saeed Soori , Konstantin Mischenko , Aryan Mokhtari , Maryam Mehri Dehnavi , Mert Gurbuzbalaban

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel Distributed-Approx Newton algorithms that approximate the standard Newton optimization method. We first develop the…

Optimization and Control · Mathematics 2019-11-21 Tor Anderson , Chin-Yao Chang , Sonia Martinez

This paper considers the problem of distributed multi-agent learning, where the global aim is to minimize a sum of local objective (empirical loss) functions through local optimization and information exchange between neighbouring nodes. We…

Optimization and Control · Mathematics 2023-07-20 Alessio Maritan , Ganesh Sharma , Luca Schenato , Subhrakanti Dey

Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…

Statistics Theory · Mathematics 2026-02-06 Antoine Godichon-Baggioni , Bruno Portier , Guillaume Sallé

This paper considers the distributed optimization problem where each node of a peer-to-peer network minimizes a finite sum of objective functions by communicating with its neighboring nodes. In sharp contrast to the existing literature…

Optimization and Control · Mathematics 2022-01-17 Jiaqi Zhang , Keyou You , Tamer Başar

Optimization problems, arise in many practical applications, from the view points of both theory and numerical methods. Especially, significant improvement in deep learning training came from the Quasi-Newton methods. Quasi-Newton search…

Optimization and Control · Mathematics 2024-11-19 Jiongcheng Li

We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the…

Optimization and Control · Mathematics 2023-06-16 Nikita Doikov , El Mahdi Chayti , Martin Jaggi