Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $\phi$- and $\beta$-Mixing

Priyanka Roy; Susanne Saminger-Platz

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arXiv · 2502.03551

Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $\phi$- and $\beta$-Mixing

Priyanka Roy·Susanne Saminger-Platz

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Abstract

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 $\phi$- and $\beta$-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.

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Priyanka Roy, Susanne Saminger-Platz. 2025-02-05. Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $\phi$- and $\beta$-Mixing. https://arxiv.org/abs/2502.03551

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