We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1]. We identify conditions that are strictly broader than previously known for polynomial convergence rate in various norms, and characterize the roles the randomness plays in determining the best multiplicative constants. Additionally, we prove almost sure convergence of the sequence.

翻译：我们在[1]中研究的无噪音回归中,在“Stochatic Gradientle Ground(SGD)算法”的启发下,我们研究了无限维度希尔伯特空间操作者组成的一组操作者随机迭接序列的趋同问题。我们确定了在各种规范中严格比以前多面趋同率所知道的要宽的条件,并确定了随机性在确定最佳多面常数方面所起的作用。此外,我们几乎可以肯定该序列的趋同性。