Mathematical Optimization for Data Science Group, Saarland University

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A Generalization Result for Convergence in Learning-to-Optimize

M. Sucker and P. Ochs

Abstract:
Convergence in learning-to-optimize is hardly studied, 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 deterministic optimization and allows for transferring geometric arguments into learning-to-optimize. 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 stationary points with high probability. This can be seen as a statistical counterpart to the use of geometric safeguards to ensure convergence. To the best of our knowledge, we are the first to prove convergence of optimization algorithms in such a probabilistic framework.



pdf	Bibtex	arXiv

Latest update: 10.10.2024

Citation:
M. Sucker, P. Ochs:
A Generalization Result for Convergence in Learning-to-Optimize.

Technical Report, ArXiv e-prints, arXiv:2410.07704, 2024.

Bibtex:
@techreport{SO24b, title = {A Generalization Result for Convergence in Learning-to-Optimize}, author = {M. Sucker and P. Ochs}, year = {2024}, journal = {ArXiv e-prints, arXiv:2410.07704}, }

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