Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training

Risheng Liu, Xuan Liu, Shangzhi Zeng, Jin Zhang, Yixuan Zhang
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:13825-13856, 2022.

Abstract

Recently, Optimization-Derived Learning (ODL) has attracted attention from learning and vision areas, which designs learning models from the perspective of optimization. However, previous ODL approaches regard the training and hyper-training procedures as two separated stages, meaning that the hyper-training variables have to be fixed during the training process, and thus it is also impossible to simultaneously obtain the convergence of training and hyper-training variables. In this work, we design a Generalized Krasnoselskii-Mann (GKM) scheme based on fixed-point iterations as our fundamental ODL module, which unifies existing ODL methods as special cases. Under the GKM scheme, a Bilevel Meta Optimization (BMO) algorithmic framework is constructed to solve the optimal training and hyper-training variables together. We rigorously prove the essential joint convergence of the fixed-point iteration for training and the process of optimizing hyper-parameters for hyper-training, both on the approximation quality, and on the stationary analysis. Experiments demonstrate the efficiency of BMO with competitive performance on sparse coding and real-world applications such as image deconvolution and rain streak removal.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-liu22j, title = {Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training}, author = {Liu, Risheng and Liu, Xuan and Zeng, Shangzhi and Zhang, Jin and Zhang, Yixuan}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {13825--13856}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/liu22j/liu22j.pdf}, url = {https://proceedings.mlr.press/v162/liu22j.html}, abstract = {Recently, Optimization-Derived Learning (ODL) has attracted attention from learning and vision areas, which designs learning models from the perspective of optimization. However, previous ODL approaches regard the training and hyper-training procedures as two separated stages, meaning that the hyper-training variables have to be fixed during the training process, and thus it is also impossible to simultaneously obtain the convergence of training and hyper-training variables. In this work, we design a Generalized Krasnoselskii-Mann (GKM) scheme based on fixed-point iterations as our fundamental ODL module, which unifies existing ODL methods as special cases. Under the GKM scheme, a Bilevel Meta Optimization (BMO) algorithmic framework is constructed to solve the optimal training and hyper-training variables together. We rigorously prove the essential joint convergence of the fixed-point iteration for training and the process of optimizing hyper-parameters for hyper-training, both on the approximation quality, and on the stationary analysis. Experiments demonstrate the efficiency of BMO with competitive performance on sparse coding and real-world applications such as image deconvolution and rain streak removal.} }
Endnote
%0 Conference Paper %T Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training %A Risheng Liu %A Xuan Liu %A Shangzhi Zeng %A Jin Zhang %A Yixuan Zhang %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-liu22j %I PMLR %P 13825--13856 %U https://proceedings.mlr.press/v162/liu22j.html %V 162 %X Recently, Optimization-Derived Learning (ODL) has attracted attention from learning and vision areas, which designs learning models from the perspective of optimization. However, previous ODL approaches regard the training and hyper-training procedures as two separated stages, meaning that the hyper-training variables have to be fixed during the training process, and thus it is also impossible to simultaneously obtain the convergence of training and hyper-training variables. In this work, we design a Generalized Krasnoselskii-Mann (GKM) scheme based on fixed-point iterations as our fundamental ODL module, which unifies existing ODL methods as special cases. Under the GKM scheme, a Bilevel Meta Optimization (BMO) algorithmic framework is constructed to solve the optimal training and hyper-training variables together. We rigorously prove the essential joint convergence of the fixed-point iteration for training and the process of optimizing hyper-parameters for hyper-training, both on the approximation quality, and on the stationary analysis. Experiments demonstrate the efficiency of BMO with competitive performance on sparse coding and real-world applications such as image deconvolution and rain streak removal.
APA
Liu, R., Liu, X., Zeng, S., Zhang, J. & Zhang, Y.. (2022). Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:13825-13856 Available from https://proceedings.mlr.press/v162/liu22j.html.

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