A Minibatch Proximal Stochastic Recursive Gradient Algorithm Using a Trust-Region-Like Scheme and Barzilai-Borwein Stepsizes

We consider the problem of minimizing the sum of an average of a large number of smooth convex component functions and a possibly nonsmooth convex function that admits a simple proximal mapping. This class of problems arises frequently in machine learning, known as regularized empirical risk minimiz...

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Main Authors: Yu, T., Liu, X.W., Dai, Y.H., Sun, Jie
Format: Journal Article
Language:English
Published: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC 2021
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/91427
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author Yu, T.
Liu, X.W.
Dai, Y.H.
Sun, Jie
author_facet Yu, T.
Liu, X.W.
Dai, Y.H.
Sun, Jie
author_sort Yu, T.
building Curtin Institutional Repository
collection Online Access
description We consider the problem of minimizing the sum of an average of a large number of smooth convex component functions and a possibly nonsmooth convex function that admits a simple proximal mapping. This class of problems arises frequently in machine learning, known as regularized empirical risk minimization (ERM). In this article, we propose mSRGTR-BB, a minibatch proximal stochastic recursive gradient algorithm, which employs a trust-region-like scheme to select stepsizes that are automatically computed by the Barzilai-Borwein method. We prove that mSRGTR-BB converges linearly in expectation for strongly and nonstrongly convex objective functions. With proper parameters, mSRGTR-BB enjoys a faster convergence rate than the state-of-the-art minibatch proximal variant of the semistochastic gradient method (mS2GD). Numerical experiments on standard data sets show that the performance of mSRGTR-BB is comparable to and sometimes even better than mS2GD with best-tuned stepsizes and is superior to some modern proximal stochastic gradient methods.
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language English
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spelling curtin-20.500.11937-914272023-05-03T07:20:45Z A Minibatch Proximal Stochastic Recursive Gradient Algorithm Using a Trust-Region-Like Scheme and Barzilai-Borwein Stepsizes Yu, T. Liu, X.W. Dai, Y.H. Sun, Jie Science & Technology Technology Computer Science, Artificial Intelligence Computer Science, Hardware & Architecture Computer Science, Theory & Methods Engineering, Electrical & Electronic Computer Science Engineering Convergence Convex functions Risk management Gradient methods Learning systems Sun Barzilai-Borwein (BB) method empirical risk minimization (ERM) proximal method stochastic gradient trust-region MACHINE We consider the problem of minimizing the sum of an average of a large number of smooth convex component functions and a possibly nonsmooth convex function that admits a simple proximal mapping. This class of problems arises frequently in machine learning, known as regularized empirical risk minimization (ERM). In this article, we propose mSRGTR-BB, a minibatch proximal stochastic recursive gradient algorithm, which employs a trust-region-like scheme to select stepsizes that are automatically computed by the Barzilai-Borwein method. We prove that mSRGTR-BB converges linearly in expectation for strongly and nonstrongly convex objective functions. With proper parameters, mSRGTR-BB enjoys a faster convergence rate than the state-of-the-art minibatch proximal variant of the semistochastic gradient method (mS2GD). Numerical experiments on standard data sets show that the performance of mSRGTR-BB is comparable to and sometimes even better than mS2GD with best-tuned stepsizes and is superior to some modern proximal stochastic gradient methods. 2021 Journal Article http://hdl.handle.net/20.500.11937/91427 10.1109/TNNLS.2020.3025383 English IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC restricted
spellingShingle Science & Technology
Technology
Computer Science, Artificial Intelligence
Computer Science, Hardware & Architecture
Computer Science, Theory & Methods
Engineering, Electrical & Electronic
Computer Science
Engineering
Convergence
Convex functions
Risk management
Gradient methods
Learning systems
Sun
Barzilai-Borwein (BB) method
empirical risk minimization (ERM)
proximal method
stochastic gradient
trust-region
MACHINE
Yu, T.
Liu, X.W.
Dai, Y.H.
Sun, Jie
A Minibatch Proximal Stochastic Recursive Gradient Algorithm Using a Trust-Region-Like Scheme and Barzilai-Borwein Stepsizes
title A Minibatch Proximal Stochastic Recursive Gradient Algorithm Using a Trust-Region-Like Scheme and Barzilai-Borwein Stepsizes
title_full A Minibatch Proximal Stochastic Recursive Gradient Algorithm Using a Trust-Region-Like Scheme and Barzilai-Borwein Stepsizes
title_fullStr A Minibatch Proximal Stochastic Recursive Gradient Algorithm Using a Trust-Region-Like Scheme and Barzilai-Borwein Stepsizes
title_full_unstemmed A Minibatch Proximal Stochastic Recursive Gradient Algorithm Using a Trust-Region-Like Scheme and Barzilai-Borwein Stepsizes
title_short A Minibatch Proximal Stochastic Recursive Gradient Algorithm Using a Trust-Region-Like Scheme and Barzilai-Borwein Stepsizes
title_sort minibatch proximal stochastic recursive gradient algorithm using a trust-region-like scheme and barzilai-borwein stepsizes
topic Science & Technology
Technology
Computer Science, Artificial Intelligence
Computer Science, Hardware & Architecture
Computer Science, Theory & Methods
Engineering, Electrical & Electronic
Computer Science
Engineering
Convergence
Convex functions
Risk management
Gradient methods
Learning systems
Sun
Barzilai-Borwein (BB) method
empirical risk minimization (ERM)
proximal method
stochastic gradient
trust-region
MACHINE
url http://hdl.handle.net/20.500.11937/91427