Stochastic gradient descent for linear least squares problems with partially observed data

TL;DR

This paper introduces a new stochastic gradient descent algorithm tailored for linear least squares problems with incomplete data, providing theoretical convergence guarantees and demonstrating effectiveness through numerical experiments.

Contribution

The paper presents a novel stochastic gradient descent method that effectively handles partially observed data in linear least squares problems, with proven convergence.

Findings

Convergence guarantees in the mean square sense.

Successful numerical validation of the method.

Effective handling of partially observed data.

Abstract

We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate at each step. Theoretical convergence guarantees in the mean square sense are provided. Numerical experiments are reported to demonstrate the theoretical findings.