research-article

A Stochastic Quasi-Newton Method for Large-Scale Optimization

Authors:

Y. SingerAuthors Info & Claims

SIAM Journal on Optimization, Volume 26, Issue 2

Pages 1008 - 1031

https://doi.org/10.1137/140954362

Published: 01 January 2016 Publication History

Abstract

The question of how to incorporate curvature information into stochastic approximation methods is challenging. The direct application of classical quasi-Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper, we propose a stochastic quasi-Newton method that is efficient, robust, and scalable. It employs the classical BFGS update formula in its limited memory form, and is based on the observation that it is beneficial to collect curvature information pointwise, and at spaced intervals. One way to do this is through (subsampled) Hessian-vector products. This technique differs from the classical approach that would compute differences of gradients at every iteration, and where controlling the quality of the curvature estimates can be difficult. We present numerical results on problems arising in machine learning that suggest that the proposed method shows much promise.

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Published In

cover image SIAM Journal on Optimization

SIAM Journal on Optimization Volume 26, Issue 2

2016

519 pages

ISSN:1052-6234

DOI:10.1137/sjope8.26.2

Issue’s Table of Contents

© 2016, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2016

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Cited By

Zampini SZerbinati UTurkyyiah GKeyes DEvans KSchenk O(2024)PETScML: Second-Order Solvers for Training Regression Problems in Scientific Machine LearningProceedings of the Platform for Advanced Scientific Computing Conference10.1145/3659914.3659931(1-12)Online publication date: 3-Jun-2024
https://dl.acm.org/doi/10.1145/3659914.3659931
Wu JHu JZhang HWen Z(2024)Convergence Analysis of an Adaptively Regularized Natural Gradient MethodIEEE Transactions on Signal Processing10.1109/TSP.2024.339849672(2527-2542)Online publication date: 9-May-2024
https://dl.acm.org/doi/10.1109/TSP.2024.3398496
Zhao MLai ZLim L(2024)Stochastic Steffensen methodComputational Optimization and Applications10.1007/s10589-024-00583-789:1(1-32)Online publication date: 7-Jun-2024
https://dl.acm.org/doi/10.1007/s10589-024-00583-7
Grieshammer MPflug LStingl MUihlein A(2024)The continuous stochastic gradient method: part I–convergence theoryComputational Optimization and Applications10.1007/s10589-023-00542-887:3(935-976)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s10589-023-00542-8
Kunstner FPortella VSchmidt MHarvey NOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Searching for optimal per-coordinate step-sizes with multidimensional backtrackingProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3666244(2725-2767)Online publication date: 10-Dec-2023
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Zhang JLiu HSo ALing Q(2023)Variance-Reduced Stochastic Quasi-Newton Methods for Decentralized LearningIEEE Transactions on Signal Processing10.1109/TSP.2023.324065271(311-326)Online publication date: 1-Jan-2023
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Yang MXu DCui QWen ZXu P(2023)An Efficient Fisher Matrix Approximation Method for Large-Scale Neural Network OptimizationIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2022.321365445:5(5391-5403)Online publication date: 1-May-2023
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Yang ZMa L(2023)Adaptive step size rules for stochastic optimization in large-scale learningStatistics and Computing10.1007/s11222-023-10218-233:2Online publication date: 20-Feb-2023
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Irwin BHaber E(2023)Secant penalized BFGS: a noise robust quasi-Newton method via penalizing the secant conditionComputational Optimization and Applications10.1007/s10589-022-00448-x84:3(651-702)Online publication date: 9-Jan-2023
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Chen SYuan YTao YCai ZYu D(2023)Resource-Adaptive Newton’s Method for Distributed LearningComputing and Combinatorics10.1007/978-3-031-49190-0_24(335-346)Online publication date: 15-Dec-2023
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