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Journal of Industrial & Management Optimization
Article . 2023 . Peer-reviewed
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Article . 2023
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Article . 2022
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A variance-reduced stochastic gradient tracking algorithm for decentralized optimization with orthogonality constraints

Authors: Wang, Lei; Liu, Xin;

A variance-reduced stochastic gradient tracking algorithm for decentralized optimization with orthogonality constraints

Abstract

Decentralized optimization with orthogonality constraints is found widely in scientific computing and data science. Since the orthogonality constraints are nonconvex, it is quite challenging to design efficient algorithms. Existing approaches leverage the geometric tools from Riemannian optimization to solve this problem at the cost of high sample and communication complexities. To relieve this difficulty, based on two novel techniques that can waive the orthogonality constraints, we propose a variance-reduced stochastic gradient tracking (VRSGT) algorithm with the convergence rate of $O(1 / k)$ to a stationary point. To the best of our knowledge, VRSGT is the first algorithm for decentralized optimization with orthogonality constraints that reduces both sampling and communication complexities simultaneously. In the numerical experiments, VRSGT has a promising performance in a real-world autonomous driving application.

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Keywords

Large-scale problems in mathematical programming, FOS: Computer and information sciences, Computer Science - Machine Learning, Stiefel manifold, variance reduction, Stochastic programming, Machine Learning (stat.ML), Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Machine Learning (cs.LG), Nonlinear programming, Statistics - Machine Learning, Optimization and Control (math.OC), orthogonality constraints, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, decentralized optimization, stochastic gradient tracking, Mathematics - Optimization and Control

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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green
gold