SABRINA: A Stochastic Subspace Majorization-Minimization Algorithm

A wide class of problems involves the minimization of a coercive and differentiable function F on R N whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradient-based optimization literature cannot be directly applied and robustne...

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Veröffentlicht in:	Journal of optimization theory and applications Jg. 195; H. 3; S. 919 - 952
Hauptverfasser:	Chouzenoux, Emilie, Fest, Jean-Baptiste
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.12.2022 Springer Nature B.V Springer Verlag
Schlagworte:	Algorithms Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Convergence Engineering Engineering Sciences Errors Image processing Machine learning Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Robustness (mathematics) Signal and Image processing Stochastic processes Subspaces Theory of Computation Subspace acceleration Majorization-minimization Stochastic optimization Binary logistic regression Image reconstruction Convergence analysis subspace acceleration binary logistic regression image reconstruction convergence analysis Majorization-Minimization
ISSN:	0022-3239, 1573-2878
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Abstract	A wide class of problems involves the minimization of a coercive and differentiable function F on R N whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradient-based optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work is dedicated to investigating the convergence of Majorization-Minimization (MM) schemes when stochastic errors affect the gradient terms. We introduce a general stochastic optimization framework, called StochAstic suBspace majoRIzation-miNimization Algorithm SABRINA that encompasses MM quadratic schemes possibly enhanced with a subspace acceleration strategy. New asymptotical results are built for the stochastic process generated by SABRINA . Two sets of numerical experiments in the field of machine learning and image processing are presented to support our theoretical results and illustrate the good performance of SABRINA with respect to state-of-the-art gradient-based stochastic optimization methods.
AbstractList	A wide class of problems involves the minimization of a coercive and differentiable function F on R N whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradientbased optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work is dedicated to investigating the convergence of Majorization-Minimization (MM) schemes when stochastic errors affect the gradient terms. We introduce a general stochastic optimization framework, called SABRINA (StochAstic suBspace majoRIzation-miNimization Algorithm) that encompasses MM quadratic schemes possibly enhanced with a subspace acceleration strategy. New asymptotical results are built for the stochastic process generated by SABRINA. Two sets of numerical experiments in the field of machine learning and image processing are presented to support our theoretical results and illustrate the good performance of SABRINA with respect to state-of-the-art gradient-based stochastic optimization methods. A wide class of problems involves the minimization of a coercive and differentiable function F on R N whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradient-based optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work is dedicated to investigating the convergence of Majorization-Minimization (MM) schemes when stochastic errors affect the gradient terms. We introduce a general stochastic optimization framework, called StochAstic suBspace majoRIzation-miNimization Algorithm SABRINA that encompasses MM quadratic schemes possibly enhanced with a subspace acceleration strategy. New asymptotical results are built for the stochastic process generated by SABRINA . Two sets of numerical experiments in the field of machine learning and image processing are presented to support our theoretical results and illustrate the good performance of SABRINA with respect to state-of-the-art gradient-based stochastic optimization methods. A wide class of problems involves the minimization of a coercive and differentiable function F on RN whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradient-based optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work is dedicated to investigating the convergence of Majorization-Minimization (MM) schemes when stochastic errors affect the gradient terms. We introduce a general stochastic optimization framework, called StochAstic suBspace majoRIzation-miNimization Algorithm SABRINA that encompasses MM quadratic schemes possibly enhanced with a subspace acceleration strategy. New asymptotical results are built for the stochastic process generated by SABRINA. Two sets of numerical experiments in the field of machine learning and image processing are presented to support our theoretical results and illustrate the good performance of SABRINA with respect to state-of-the-art gradient-based stochastic optimization methods.
Author	Chouzenoux, Emilie Fest, Jean-Baptiste
Author_xml	– sequence: 1 givenname: Emilie orcidid: 0000-0003-3631-6093 surname: Chouzenoux fullname: Chouzenoux, Emilie organization: Centre de Vision Numérique, Inria, CentraleSupélec, Université Paris-Saclay – sequence: 2 givenname: Jean-Baptiste surname: Fest fullname: Fest, Jean-Baptiste email: jean-baptiste.fest@centralesupelec.fr organization: Centre de Vision Numérique, Inria, CentraleSupélec, Université Paris-Saclay
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Keywords	Subspace acceleration Majorization-minimization Stochastic optimization Binary logistic regression Image reconstruction Convergence analysis subspace acceleration binary logistic regression image reconstruction convergence analysis Majorization-Minimization
Language	English
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Title	SABRINA: A Stochastic Subspace Majorization-Minimization Algorithm
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