Lovas, Attila and Rásonyi, Miklós (2023) Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics. APPLIED MATHEMATICS AND OPTIMIZATION, 88 (3). ISSN 0095-4616
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Official URL: https://doi.org/10.1007/s00245-023-10052-y
Abstract
We study the mixing properties of an important optimization algorithm of machine learning: the stochastic gradient Langevin dynamics (SGLD) with a fixed step size. The data stream is not assumed to be independent hence the SGLD is not a Markov chain, merely a Markov chain in a random environment, which complicates the mathematical treatment considerably. We derive a strong law of large numbers and a functional central limit theorem for SGLD.
| Item Type: | Article |
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| Uncontrolled Keywords: | Stochastic gradient descent, Online learning, Functional central limit theorem, Mixing, Markov chains in random environments |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 03 Apr 2024 07:27 |
| Last Modified: | 03 Apr 2024 07:27 |
| URI: | https://real.mtak.hu/id/eprint/191455 |
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