arXiv:2502.03551stat.MLcs.LG2025-02被引 1
研究马尔可夫链下希尔伯特空间梯度下降的收敛性
Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $ϕ$- and $β$-Mixing
- 在一般希尔伯特空间中分析马尔可夫链梯度下降
- 给出ϕ-和β-混合系数指数与多项式衰减下的收敛上界
- 适用于非独立数据场景下的优化理论研究
本文研究在一般希尔伯特空间中运行的严格平稳马尔可夫链梯度下降算法。分析聚焦于底层过程的混合系数，特别是ϕ-和β-混合系数。在这些假设下，基于混合系数的指数衰减和多项式衰减，推导出算法收敛行为的概率上界。
原文摘要 · Abstract (English)
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.
优化理论马尔可夫链收敛性分析
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