• Corpus ID: 246608260

Polynomial convergence of iterations of certain random operators in Hilbert space

  title={Polynomial convergence of iterations of certain random operators in Hilbert space},
  author={Soumyadip Ghosh and Ying-Ling Lu and Tomasz Nowicki},
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 stud-ied 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… 



Tight Nonparametric Convergence Rates for Stochastic Gradient Descent under the Noiseless Linear Model

This work analyzes the convergence of single-pass, fixed step-size stochastic gradient descent on the least-square risk under the noiseless linear model and applies the analysis beyond the supervised learning setting to obtain convergence rates for the averaging process on a graph depending on its spectral dimension.

Functional Analysis, Methods of Modern Mathematical Physics

  • Elsevier Science,
  • 1981

Martingale Limit Theory and Its Application

Functional Analysis I

A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with

A Series of Modern Surveys in Mathematics

Gaussian free fields for mathematicians

The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the