Linearly convergent bilevel optimization with single-step inner methods
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to solve the full-system optimality conditions, but to precondit...
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| Published in | Computational optimization and applications Vol. 87; no. 2; pp. 571 - 610 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.03.2024
Springer Nature B.V |
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| Abstract | We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to solve the full-system optimality conditions, but to precondition them to alternate between taking steps of simple conventional methods for the inner problem, the adjoint equation, and the outer problem. While the inner objective has to be smooth, the outer objective may be nonsmooth subject to a prox-contractivity condition. We prove
linear convergence
of the approach for combinations of gradient descent and forward-backward splitting with exact and inexact solution of the adjoint equation. We demonstrate good performance on learning the regularization parameter for anisotropic total variation image denoising, and the convolution kernel for image deconvolution. |
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| AbstractList | We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to solve the full-system optimality conditions, but to precondition them to alternate between taking steps of simple conventional methods for the inner problem, the adjoint equation, and the outer problem. While the inner objective has to be smooth, the outer objective may be nonsmooth subject to a prox-contractivity condition. We prove linear convergence of the approach for combinations of gradient descent and forward-backward splitting with exact and inexact solution of the adjoint equation. We demonstrate good performance on learning the regularization parameter for anisotropic total variation image denoising, and the convolution kernel for image deconvolution. We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to solve the full-system optimality conditions, but to precondition them to alternate between taking steps of simple conventional methods for the inner problem, the adjoint equation, and the outer problem. While the inner objective has to be smooth, the outer objective may be nonsmooth subject to a prox-contractivity condition. We prove linear convergence of the approach for combinations of gradient descent and forward-backward splitting with exact and inexact solution of the adjoint equation. We demonstrate good performance on learning the regularization parameter for anisotropic total variation image denoising, and the convolution kernel for image deconvolution. |
| Author | Suonperä, Ensio Valkonen, Tuomo |
| Author_xml | – sequence: 1 givenname: Ensio orcidid: 0000-0002-2111-0239 surname: Suonperä fullname: Suonperä, Ensio email: ensio.suonpera@helsinki.fi organization: Department of Mathematics and Statistics, University of Helsinki – sequence: 2 givenname: Tuomo surname: Valkonen fullname: Valkonen, Tuomo organization: Department of Mathematics and Statistics, University of Helsinki, ModeMat, Escuela Politécnica Nacional |
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| CitedBy_id | crossref_primary_10_1007_s10589_024_00587_3 |
| Cites_doi | 10.1007/s00245-018-9541-6 10.1007/s10851-016-0663-7 10.1007/s10107-012-0535-x 10.1080/02331939508844060 10.1088/0266-5611/30/5/055012 10.1016/j.amc.2012.10.010 10.1017/CBO9780511983658 10.1007/s10851-017-0736-2 10.1137/18M1170194 10.1007/bf01585928 10.1080/10556788.2019.1619729 10.1016/j.jmaa.2015.09.023 10.1007/s10851-016-0662-8 10.1137/0913035 10.1137/16m105592x 10.1109/TMI.2020.3017353 10.1007/s10851-021-01020-8 10.1287/moor.2021.1122 10.1137/120882706 10.1137/100814494 10.1007/s10589-020-00254-3 10.1007/s10107-011-0508-5 10.3934/ipi.2015.9.1139 10.1137/20m1377199 10.1088/1361-6420/aade77 10.1007/s10851-010-0251-1 10.1016/0305-0548(82)90007-7 10.1007/s11228-016-0371-x 10.1137/21M143412X 10.1007/978-981-10-4774-9 10.1137/1.9781611971309 10.5281/zenodo.7974062 10.1007/978-3-662-45827-3 10.1609/aaai.v36i7.20706 10.1515/9783110430394-008 10.1007/978-3-662-45504-3_8 10.1287/moor.2021.1164 10.1007/978-3-030-52119-6 10.1007/978-3-030-03009-4_93-1 |
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| References | De Los Reyes, Schönlieb, Valkonen (CR42) 2017; 57 CR39 CR34 CR33 CR32 CR30 Fliege, Tin, Zemkoho (CR3) 2021; 78 Chambolle, Pock (CR16) 2011; 40 CR5 Ehrhardt, Roberts (CR15) 2021 De Los Reyes, Schönlieb, Valkonen (CR43) 2016; 434 CR49 Chambolle, Pock (CR45) 2021; 14 CR47 Allende, Still (CR2) 2012; 138 Ochs, Ranftl, Brox, Pock (CR46) 2016; 56 Dempe (CR31) 2006 Luo, Pang, Ralph (CR29) 1996 Sabach, Shtern (CR40) 2017; 27 Hare, Lewis (CR48) 2004; 11 Kunisch, Pock (CR8) 2013; 6 Valkonen (CR53) 2014; 30 Sherry, Benning, De los Reyes, Graves, Maierhofer, Williams, Schönlieb, Ehrhardt (CR11) 2020; 39 CR19 Hintermüller, Wu (CR44) 2015; 9 Jiang, Li, Huang, Wu (CR4) 2013; 219 CR14 De Los Reyes, Schönlieb (CR7) 2013; 7 CR13 CR12 Dempe, Zemkoho (CR37) 2012; 138 CR54 Hintermüller, Rautenberg, Wu, Langer (CR10) 2017; 59 CR51 CR50 Mehlitz, Zemkoho (CR38) 2021 Zemkoho (CR36) 2016; 24 He, Yuan (CR17) 2012; 5 Clason, Mazurenko, Valkonen (CR52) 2019; 29 Holler, Kunisch, Barnard (CR9) 2018; 34 CR28 CR26 CR25 CR23 Ye, Zhu (CR35) 1995; 33 CR22 CR21 Valkonen (CR18) 2020; 82 CR20 Yang, Ji, Liang (CR24) 2021; 34 Ji, Liang (CR27) 2022; 23 Bard, Falk (CR1) 1982; 9 Shehu, Vuong, Zemkoho (CR41) 2019; 36 Van der Vorst (CR55) 1992; 13 Falk, Liu (CR6) 1995; 70 S Sabach (527_CR40) 2017; 27 A Chambolle (527_CR45) 2021; 14 S Dempe (527_CR37) 2012; 138 JC De Los Reyes (527_CR7) 2013; 7 527_CR5 JF Bard (527_CR1) 1982; 9 527_CR28 527_CR26 AB Zemkoho (527_CR36) 2016; 24 527_CR20 527_CR21 GB Allende (527_CR2) 2012; 138 JE Falk (527_CR6) 1995; 70 527_CR25 527_CR22 527_CR23 WL Hare (527_CR48) 2004; 11 B He (527_CR17) 2012; 5 P Ochs (527_CR46) 2016; 56 C Clason (527_CR52) 2019; 29 M Hintermüller (527_CR10) 2017; 59 527_CR39 ZQ Luo (527_CR29) 1996 S Dempe (527_CR31) 2006 527_CR32 527_CR30 J Yang (527_CR24) 2021; 34 A Chambolle (527_CR16) 2011; 40 527_CR33 527_CR34 F Sherry (527_CR11) 2020; 39 T Valkonen (527_CR18) 2020; 82 527_CR49 K Ji (527_CR27) 2022; 23 K Kunisch (527_CR8) 2013; 6 JC De Los Reyes (527_CR42) 2017; 57 527_CR47 MJ Ehrhardt (527_CR15) 2021 JJ Ye (527_CR35) 1995; 33 T Valkonen (527_CR53) 2014; 30 J Fliege (527_CR3) 2021; 78 HA Van der Vorst (527_CR55) 1992; 13 527_CR50 G Holler (527_CR9) 2018; 34 M Hintermüller (527_CR44) 2015; 9 527_CR19 Y Shehu (527_CR41) 2019; 36 P Mehlitz (527_CR38) 2021 Y Jiang (527_CR4) 2013; 219 527_CR54 527_CR51 JC De Los Reyes (527_CR43) 2016; 434 527_CR13 527_CR14 527_CR12 |
| References_xml | – ident: CR22 – volume: 82 start-page: 1 issue: 2 year: 2020 ident: CR18 article-title: Testing and non-linear preconditioning of the proximal point method publication-title: Appl. Math. Optim. doi: 10.1007/s00245-018-9541-6 – volume: 56 start-page: 175 issue: 2 year: 2016 end-page: 194 ident: CR46 article-title: Techniques for gradient-based bilevel optimization with non-smooth lower level problems publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-016-0663-7 – ident: CR49 – ident: CR39 – ident: CR51 – volume: 138 start-page: 309 issue: 1–2 year: 2012 end-page: 332 ident: CR2 article-title: Solving bilevel programs with the KKT-approach publication-title: Math. Program. doi: 10.1007/s10107-012-0535-x – ident: CR12 – volume: 33 start-page: 9 issue: 1 year: 1995 end-page: 27 ident: CR35 article-title: Optimality conditions for bilevel programming problems publication-title: Optimization doi: 10.1080/02331939508844060 – ident: CR54 – volume: 30 issue: 5 year: 2014 ident: CR53 article-title: A primal-dual hybrid gradient method for non-linear operators with applications to MRI publication-title: Inverse Prob. doi: 10.1088/0266-5611/30/5/055012 – volume: 219 start-page: 4332 issue: 9 year: 2013 end-page: 4339 ident: CR4 article-title: Application of particle swarm optimization based on CHKS smoothing function for solving nonlinear bilevel programming problem publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2012.10.010 – ident: CR25 – year: 1996 ident: CR29 publication-title: Mathematical Programs with Equilibrium Constraints doi: 10.1017/CBO9780511983658 – volume: 59 start-page: 515 year: 2017 ident: CR10 article-title: Optimal selection of the regularization function in a weighted total variation model. Part II: algorithm, its analysis and numerical tests publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-017-0736-2 – ident: CR21 – volume: 29 start-page: 933 year: 2019 end-page: 963 ident: CR52 article-title: Acceleration and global convergence of a first-order primal-dual method for nonconvex problems publication-title: SIAM J. Optim. doi: 10.1137/18M1170194 – ident: CR19 – volume: 70 start-page: 47 issue: 1–3 year: 1995 end-page: 72 ident: CR6 article-title: On bilevel programming, Part I: general nonlinear cases publication-title: Math. Program. doi: 10.1007/bf01585928 – volume: 36 start-page: 1 issue: 1 year: 2019 end-page: 19 ident: CR41 article-title: An inertial extrapolation method for convex simple bilevel optimization publication-title: Optim. Methods Softw. doi: 10.1080/10556788.2019.1619729 – ident: CR50 – volume: 34 start-page: 13670 year: 2021 end-page: 13682 ident: CR24 article-title: Provably faster algorithms for bilevel optimization publication-title: Adv. Neural. Inf. Process. Syst. – ident: CR32 – volume: 434 start-page: 464 year: 2016 end-page: 500 ident: CR43 article-title: The structure of optimal parameters for image restoration problems publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.09.023 – ident: CR5 – volume: 57 start-page: 1 year: 2017 end-page: 25 ident: CR42 article-title: Bilevel parameter learning for higher-order total variation regularisation models publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-016-0662-8 – volume: 13 start-page: 631 issue: 2 year: 1992 end-page: 644 ident: CR55 article-title: Bi-cgstab: a fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems publication-title: SIAM J. Sci. Comput. doi: 10.1137/0913035 – ident: CR26 – volume: 27 start-page: 640 issue: 2 year: 2017 end-page: 660 ident: CR40 article-title: A first order method for solving convex bilevel optimization problems publication-title: SIAM J. Optim. doi: 10.1137/16m105592x – ident: CR47 – ident: CR14 – volume: 39 start-page: 4310 issue: 12 year: 2020 end-page: 4321 ident: CR11 article-title: Learning the sampling pattern for MRI publication-title: IEEE Trans. Med. Imaging doi: 10.1109/TMI.2020.3017353 – ident: CR30 – year: 2006 ident: CR31 publication-title: Foundations of Bilevel Programming. Nonconvex Optimization and Its Applications – volume: 7 start-page: 1183 year: 2013 end-page: 1214 ident: CR7 article-title: Image denoising: learning noise distribution via PDE-constrained optimization publication-title: Inverse Prob. Imag. – ident: CR33 – volume: 11 start-page: 251 issue: 2 year: 2004 end-page: 266 ident: CR48 article-title: Identifying active constraints via partial smoothness and prox-regularity publication-title: J. Convex Anal. – volume: 23 start-page: 1 year: 2022 end-page: 56 ident: CR27 article-title: Lower bounds and accelerated algorithms for bilevel optimization publication-title: J. Mach. Learn. Res. – year: 2021 ident: CR15 article-title: Inexact derivative-free optimization for bilevel learning publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-021-01020-8 – year: 2021 ident: CR38 article-title: Sufficient optimality conditions in bilevel programming publication-title: Math. Oper. Res. doi: 10.1287/moor.2021.1122 – volume: 6 start-page: 938 issue: 2 year: 2013 end-page: 983 ident: CR8 article-title: A bilevel optimization approach for parameter learning in variational models publication-title: SIAM J. Imag. Sci. doi: 10.1137/120882706 – volume: 5 start-page: 119 issue: 1 year: 2012 end-page: 149 ident: CR17 article-title: Convergence analysis of primal-dual algorithms for a saddle-point problem: from contraction perspective publication-title: SIAM J. Imag. Sci. doi: 10.1137/100814494 – ident: CR23 – volume: 78 start-page: 793 year: 2021 end-page: 824 ident: CR3 article-title: Gauss-newton-type methods for bilevel optimization publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-020-00254-3 – volume: 138 start-page: 447 issue: 1–2 year: 2012 end-page: 473 ident: CR37 article-title: The bilevel programming problem: reformulations, constraint qualifications and optimality conditions publication-title: Math. Program. doi: 10.1007/s10107-011-0508-5 – volume: 9 start-page: 1139 issue: 4 year: 2015 end-page: 1169 ident: CR44 article-title: Bilevel optimization for calibrating point spread functions in blind deconvolution publication-title: Inverse Probl. Imag. doi: 10.3934/ipi.2015.9.1139 – volume: 14 start-page: 778 issue: 2 year: 2021 end-page: 813 ident: CR45 article-title: Learning consistent discretizations of the total variation publication-title: SIAM J. Imag. Sci. doi: 10.1137/20m1377199 – ident: CR13 – volume: 34 issue: 11 year: 2018 ident: CR9 article-title: A bilevel approach for parameter learning in inverse problems publication-title: Inverse Prob. doi: 10.1088/1361-6420/aade77 – volume: 40 start-page: 120 year: 2011 end-page: 145 ident: CR16 article-title: A first-order primal-dual algorithm for convex problems with applications to imaging publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-010-0251-1 – ident: CR34 – volume: 9 start-page: 77 issue: 1 year: 1982 end-page: 100 ident: CR1 article-title: An explicit solution to the multi-level programming problem publication-title: Comput. Oper. Res. doi: 10.1016/0305-0548(82)90007-7 – ident: CR28 – volume: 24 start-page: 423 issue: 3 year: 2016 end-page: 448 ident: CR36 article-title: Solving ill-posed bilevel programs publication-title: Set-valued Var. Anal. doi: 10.1007/s11228-016-0371-x – ident: CR20 – volume: 13 start-page: 631 issue: 2 year: 1992 ident: 527_CR55 publication-title: SIAM J. Sci. Comput. doi: 10.1137/0913035 – volume: 34 issue: 11 year: 2018 ident: 527_CR9 publication-title: Inverse Prob. doi: 10.1088/1361-6420/aade77 – volume: 59 start-page: 515 year: 2017 ident: 527_CR10 publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-017-0736-2 – volume: 138 start-page: 447 issue: 1–2 year: 2012 ident: 527_CR37 publication-title: Math. Program. doi: 10.1007/s10107-011-0508-5 – ident: 527_CR5 – ident: 527_CR13 – ident: 527_CR49 – ident: 527_CR26 – ident: 527_CR51 – ident: 527_CR14 doi: 10.1137/21M143412X – volume: 138 start-page: 309 issue: 1–2 year: 2012 ident: 527_CR2 publication-title: Math. Program. doi: 10.1007/s10107-012-0535-x – ident: 527_CR30 doi: 10.1007/978-981-10-4774-9 – volume: 29 start-page: 933 year: 2019 ident: 527_CR52 publication-title: SIAM J. Optim. doi: 10.1137/18M1170194 – ident: 527_CR22 – volume: 70 start-page: 47 issue: 1–3 year: 1995 ident: 527_CR6 publication-title: Math. Program. doi: 10.1007/bf01585928 – year: 2021 ident: 527_CR15 publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-021-01020-8 – ident: 527_CR47 doi: 10.1137/1.9781611971309 – volume: 82 start-page: 1 issue: 2 year: 2020 ident: 527_CR18 publication-title: Appl. Math. Optim. doi: 10.1007/s00245-018-9541-6 – volume: 6 start-page: 938 issue: 2 year: 2013 ident: 527_CR8 publication-title: SIAM J. Imag. Sci. doi: 10.1137/120882706 – volume: 78 start-page: 793 year: 2021 ident: 527_CR3 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-020-00254-3 – volume: 219 start-page: 4332 issue: 9 year: 2013 ident: 527_CR4 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2012.10.010 – ident: 527_CR54 doi: 10.5281/zenodo.7974062 – volume: 5 start-page: 119 issue: 1 year: 2012 ident: 527_CR17 publication-title: SIAM J. Imag. Sci. doi: 10.1137/100814494 – volume: 57 start-page: 1 year: 2017 ident: 527_CR42 publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-016-0662-8 – volume: 56 start-page: 175 issue: 2 year: 2016 ident: 527_CR46 publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-016-0663-7 – volume: 34 start-page: 13670 year: 2021 ident: 527_CR24 publication-title: Adv. Neural. Inf. Process. Syst. – ident: 527_CR32 doi: 10.1007/978-3-662-45827-3 – ident: 527_CR25 – volume: 30 issue: 5 year: 2014 ident: 527_CR53 publication-title: Inverse Prob. doi: 10.1088/0266-5611/30/5/055012 – volume: 40 start-page: 120 year: 2011 ident: 527_CR16 publication-title: J. Math. Imag. Vis. doi: 10.1007/s10851-010-0251-1 – volume: 23 start-page: 1 year: 2022 ident: 527_CR27 publication-title: J. Mach. Learn. Res. – volume: 24 start-page: 423 issue: 3 year: 2016 ident: 527_CR36 publication-title: Set-valued Var. Anal. doi: 10.1007/s11228-016-0371-x – volume-title: Foundations of Bilevel Programming. Nonconvex Optimization and Its Applications year: 2006 ident: 527_CR31 – volume: 36 start-page: 1 issue: 1 year: 2019 ident: 527_CR41 publication-title: Optim. Methods Softw. doi: 10.1080/10556788.2019.1619729 – ident: 527_CR21 – ident: 527_CR23 doi: 10.1609/aaai.v36i7.20706 – ident: 527_CR50 doi: 10.1515/9783110430394-008 – volume-title: Mathematical Programs with Equilibrium Constraints year: 1996 ident: 527_CR29 doi: 10.1017/CBO9780511983658 – ident: 527_CR12 doi: 10.1007/978-3-662-45504-3_8 – ident: 527_CR19 – volume: 27 start-page: 640 issue: 2 year: 2017 ident: 527_CR40 publication-title: SIAM J. Optim. doi: 10.1137/16m105592x – ident: 527_CR39 doi: 10.1287/moor.2021.1164 – volume: 7 start-page: 1183 year: 2013 ident: 527_CR7 publication-title: Inverse Prob. Imag. – ident: 527_CR34 doi: 10.1007/978-3-030-52119-6 – volume: 33 start-page: 9 issue: 1 year: 1995 ident: 527_CR35 publication-title: Optimization doi: 10.1080/02331939508844060 – ident: 527_CR20 doi: 10.1007/978-3-030-03009-4_93-1 – year: 2021 ident: 527_CR38 publication-title: Math. Oper. Res. doi: 10.1287/moor.2021.1122 – ident: 527_CR28 – volume: 11 start-page: 251 issue: 2 year: 2004 ident: 527_CR48 publication-title: J. Convex Anal. – volume: 434 start-page: 464 year: 2016 ident: 527_CR43 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.09.023 – volume: 9 start-page: 1139 issue: 4 year: 2015 ident: 527_CR44 publication-title: Inverse Probl. Imag. doi: 10.3934/ipi.2015.9.1139 – ident: 527_CR33 – volume: 14 start-page: 778 issue: 2 year: 2021 ident: 527_CR45 publication-title: SIAM J. Imag. Sci. doi: 10.1137/20m1377199 – volume: 39 start-page: 4310 issue: 12 year: 2020 ident: 527_CR11 publication-title: IEEE Trans. Med. Imaging doi: 10.1109/TMI.2020.3017353 – volume: 9 start-page: 77 issue: 1 year: 1982 ident: 527_CR1 publication-title: Comput. Oper. Res. doi: 10.1016/0305-0548(82)90007-7 |
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| Title | Linearly convergent bilevel optimization with single-step inner methods |
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