@article{eb6a1e98381b44ce91f663dbe90fa0a8,
title = "Universal halting times in optimization and machine learning",
abstract = "We present empirical evidence that the halting times for a class of optimization algorithms are universal. The algorithms we consider come from quadratic optimization, spin glasses and machine learning. A universality theorem is given in the case of the quadratic gradient descent flow. More precisely, given an algorithm, which we take to be both the optimization routine and the form of the random landscape, the fluctuations of the halting time of the algorithm follow a distribution that, after centering and scaling, appears invariant under changes in the distribution on the landscape - universality is present.",
author = "Levent Sagun and Thomas Trogdon and Yann Lecun",
note = "Funding Information: Acknowledgments. We thank Percy Deift and Andrew Stuart for valuable discussions and G{\'e}rard Ben Arous for his mentorship throughout the process of this research. The first author thanks U˘gur G{\"u}ney very much for his availability, support and valuable contributions in countless implementation issues. This work was partially supported by the National Science Foundation under grant number DMS-1303018 (TT). Funding Information: We thank Percy Deift and Andrew Stuart for valuable discussions and G{\'e}rard Ben Arous for his mentorship throughout the process of this research. The first author thanks Uğur G{\"u}ney very much for his availability, support and valuable contributions in countless implementation issues. This work was partially supported by the National Science Foundation under grant number DMS-1303018 (TT).",
year = "2018",
doi = "10.1090/qam/1483",
language = "English (US)",
volume = "76",
pages = "289--301",
journal = "Quarterly of Applied Mathematics",
issn = "0033-569X",
publisher = "American Mathematical Society",
number = "2",
}