Towards Constituting Mathematical Structures for Learning to Optimize

Jialin Liu, Xiaohan Chen, Zhangyang Wang, Wotao Yin, Hanqin Cai
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:21426-21449, 2023.

Abstract

Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-liu23e, title = {Towards Constituting Mathematical Structures for Learning to Optimize}, author = {Liu, Jialin and Chen, Xiaohan and Wang, Zhangyang and Yin, Wotao and Cai, Hanqin}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {21426--21449}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/liu23e/liu23e.pdf}, url = {https://proceedings.mlr.press/v202/liu23e.html}, abstract = {Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.} }
Endnote
%0 Conference Paper %T Towards Constituting Mathematical Structures for Learning to Optimize %A Jialin Liu %A Xiaohan Chen %A Zhangyang Wang %A Wotao Yin %A Hanqin Cai %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-liu23e %I PMLR %P 21426--21449 %U https://proceedings.mlr.press/v202/liu23e.html %V 202 %X Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.
APA
Liu, J., Chen, X., Wang, Z., Yin, W. & Cai, H.. (2023). Towards Constituting Mathematical Structures for Learning to Optimize. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:21426-21449 Available from https://proceedings.mlr.press/v202/liu23e.html.

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