A Generalization Result for Convergence in Learning-to-Optimize

Michael Sucker, Peter Ochs
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:57212-57230, 2025.

Abstract

Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that the outcome cannot be reliably assured. Especially, convergence is hardly studied in learning-to-optimize, because conventional convergence guarantees in optimization are based on geometric arguments, which cannot be applied easily to learned algorithms. Thus, we develop a probabilistic framework that resembles classical optimization and allows for transferring geometric arguments into learning-to-optimize. Based on our new proof-strategy, our main theorem is a generalization result for parametric classes of potentially non-smooth, non-convex loss functions and establishes the convergence of learned optimization algorithms to critical points with high probability. This effectively generalizes the results of a worst-case analysis into a probabilistic framework, and frees the design of the learned algorithm from using safeguards.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-sucker25a, title = {A Generalization Result for Convergence in Learning-to-Optimize}, author = {Sucker, Michael and Ochs, Peter}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {57212--57230}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/sucker25a/sucker25a.pdf}, url = {https://proceedings.mlr.press/v267/sucker25a.html}, abstract = {Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that the outcome cannot be reliably assured. Especially, convergence is hardly studied in learning-to-optimize, because conventional convergence guarantees in optimization are based on geometric arguments, which cannot be applied easily to learned algorithms. Thus, we develop a probabilistic framework that resembles classical optimization and allows for transferring geometric arguments into learning-to-optimize. Based on our new proof-strategy, our main theorem is a generalization result for parametric classes of potentially non-smooth, non-convex loss functions and establishes the convergence of learned optimization algorithms to critical points with high probability. This effectively generalizes the results of a worst-case analysis into a probabilistic framework, and frees the design of the learned algorithm from using safeguards.} }
Endnote
%0 Conference Paper %T A Generalization Result for Convergence in Learning-to-Optimize %A Michael Sucker %A Peter Ochs %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-sucker25a %I PMLR %P 57212--57230 %U https://proceedings.mlr.press/v267/sucker25a.html %V 267 %X Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that the outcome cannot be reliably assured. Especially, convergence is hardly studied in learning-to-optimize, because conventional convergence guarantees in optimization are based on geometric arguments, which cannot be applied easily to learned algorithms. Thus, we develop a probabilistic framework that resembles classical optimization and allows for transferring geometric arguments into learning-to-optimize. Based on our new proof-strategy, our main theorem is a generalization result for parametric classes of potentially non-smooth, non-convex loss functions and establishes the convergence of learned optimization algorithms to critical points with high probability. This effectively generalizes the results of a worst-case analysis into a probabilistic framework, and frees the design of the learned algorithm from using safeguards.
APA
Sucker, M. & Ochs, P.. (2025). A Generalization Result for Convergence in Learning-to-Optimize. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:57212-57230 Available from https://proceedings.mlr.press/v267/sucker25a.html.

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