Mathematical Optimization for Data Science Group, Saarland University

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Mathematical Optimization for Data Science Group

Department of Mathematics and Computer Science, Saarland University, Germany

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A Probabilistic Framework for Learnable Optimization Algorithms

P. Ochs and M. Sucker

Abstract:
We propose a statistical-learning framework for optimization algorithms. The framework is based on probability distributions over optimization trajectories induced by a distribution of optimization problems and a learnable optimization algorithm. Within this setting, optimization performance is represented through measurable performance functionals, including stopping times, contraction factors, and trajectory-level properties. The resulting framework provides a statistical perspective on optimization algorithms, allows their performance to be studied at the population level, and naturally accommodates the learning of optimization algorithms from data. Moreover, it enables the application of statistical-learning techniques to optimization, including PAC-Bayesian generalization guarantees for bounded optimization-specific performance measures. Experiments on convex, non-smooth, non-convex, and stochastic optimization problems illustrate the framework and demonstrate the statistical nature of optimization performance.



pdf	Bibtex	arXiv

Latest update: 17.08.2026

Citation:
P. Ochs, M. Sucker:
A Probabilistic Framework for Learnable Optimization Algorithms.

Technical Report, ArXiv e-prints, arXiv:2408.11629, 2026.

Bibtex:
@techreport{OS26, title = {A Probabilistic Framework for Learnable Optimization Algorithms}, author = {P. Ochs and M. Sucker}, year = {2026}, journal = {ArXiv e-prints, arXiv:2408.11629}, }

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