Markov Chain Gradient Descent in Hilbert Spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908709665374208 |
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| author | Roy, Priyanka Saminger-Platz, Susanne |
| author_facet | Roy, Priyanka Saminger-Platz, Susanne |
| contents | In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We further extend these results to an online regularized learning algorithm in reproducing kernel Hilbert spaces, where the samples are drawn along a Markov chain trajectory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Markov Chain Gradient Descent in Hilbert Spaces Roy, Priyanka Saminger-Platz, Susanne Machine Learning Functional Analysis 60J20, 68T05, 68Q32, 62L20 In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We further extend these results to an online regularized learning algorithm in reproducing kernel Hilbert spaces, where the samples are drawn along a Markov chain trajectory. |
| title | Markov Chain Gradient Descent in Hilbert Spaces |
| topic | Machine Learning Functional Analysis 60J20, 68T05, 68Q32, 62L20 |
| url | https://arxiv.org/abs/2410.08361 |