论文标题
希尔伯特空间中某些随机运算符的迭代的多项式收敛
Polynomial convergence of iterations of certain random operators in Hilbert space
论文作者
论文摘要
我们研究了在[1]中研究的无噪声回归的情况下，在[1]中研究的情况下，在无噪声回归的情况下，由随机梯度下降（SGD）算法的启发，研究了一组运算符家族在无限尺寸希尔伯特空间上的随机迭代序列的收敛。我们确定的条件比以前在各种规范中以多项式收敛速率而闻名的条件更广泛，并表征了随机性在确定最佳乘法常数中所起的作用。此外，我们证明了序列的收敛几乎确定。
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.
