PAC-Bayesian Learning of Optimization Algorithms

Michael Sucker, Peter Ochs
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:8145-8164, 2023.

Abstract

We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off between a high probability of convergence and a high convergence speed. Even in the limit case, where convergence is guaranteed, our learned optimization algorithms provably outperform related algorithms based on a (deterministic) worst-case analysis. Our results rely on PAC-Bayes bounds for general, unbounded loss-functions based on exponential families. By generalizing existing ideas, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum, which enables the algorithmic realization of the learning procedure. As a proof-of-concept, we learn hyperparameters of standard optimization algorithms to empirically underline our theory.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-sucker23a, title = {PAC-Bayesian Learning of Optimization Algorithms}, author = {Sucker, Michael and Ochs, Peter}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {8145--8164}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/sucker23a/sucker23a.pdf}, url = {https://proceedings.mlr.press/v206/sucker23a.html}, abstract = {We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off between a high probability of convergence and a high convergence speed. Even in the limit case, where convergence is guaranteed, our learned optimization algorithms provably outperform related algorithms based on a (deterministic) worst-case analysis. Our results rely on PAC-Bayes bounds for general, unbounded loss-functions based on exponential families. By generalizing existing ideas, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum, which enables the algorithmic realization of the learning procedure. As a proof-of-concept, we learn hyperparameters of standard optimization algorithms to empirically underline our theory.} }
Endnote
%0 Conference Paper %T PAC-Bayesian Learning of Optimization Algorithms %A Michael Sucker %A Peter Ochs %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-sucker23a %I PMLR %P 8145--8164 %U https://proceedings.mlr.press/v206/sucker23a.html %V 206 %X We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off between a high probability of convergence and a high convergence speed. Even in the limit case, where convergence is guaranteed, our learned optimization algorithms provably outperform related algorithms based on a (deterministic) worst-case analysis. Our results rely on PAC-Bayes bounds for general, unbounded loss-functions based on exponential families. By generalizing existing ideas, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum, which enables the algorithmic realization of the learning procedure. As a proof-of-concept, we learn hyperparameters of standard optimization algorithms to empirically underline our theory.
APA
Sucker, M. & Ochs, P.. (2023). PAC-Bayesian Learning of Optimization Algorithms. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:8145-8164 Available from https://proceedings.mlr.press/v206/sucker23a.html.

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