Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $ϕ$- and $β$-Mixing
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915444595621888 |
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| author | Roy, Priyanka Saminger-Platz, Susanne |
| author_facet | Roy, Priyanka Saminger-Platz, Susanne |
| contents | In this paper, we study a strictly stationary Markov chain gradient descent algorithm operating in general Hilbert spaces. Our analysis focuses on the mixing coefficients of the underlying process, specifically the $ϕ$- and $β$-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds on the convergence behavior of the algorithm based on the exponential as well as the polynomial decay of the mixing coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $ϕ$- and $β$-Mixing Roy, Priyanka Saminger-Platz, Susanne Machine Learning Functional Analysis 60J20, 68T05, 68Q32, 62L20 In this paper, we study a strictly stationary Markov chain gradient descent algorithm operating in general Hilbert spaces. Our analysis focuses on the mixing coefficients of the underlying process, specifically the $ϕ$- and $β$-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds on the convergence behavior of the algorithm based on the exponential as well as the polynomial decay of the mixing coefficients. |
| title | Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $ϕ$- and $β$-Mixing |
| topic | Machine Learning Functional Analysis 60J20, 68T05, 68Q32, 62L20 |
| url | https://arxiv.org/abs/2502.03551 |