Stochastic Variance Reduced Gradient for affine rank minimization problem

TL;DR

This paper introduces a stochastic variance reduced gradient algorithm for affine rank minimization, improving efficiency and convergence speed while maintaining accuracy, and demonstrating superior performance over existing methods.

Contribution

It presents a novel stochastic gradient method with variance reduction for affine rank minimization, with proven linear convergence under restricted isometry conditions.

Findings

Algorithm converges linearly in expectation.

Outperforms state-of-the-art greedy algorithms in efficiency and accuracy.

Balances efficiency, adaptivity, and precision effectively.

Abstract

We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic gradient descent strategy enjoys a more favorable complexity than full gradients. It also reduces the variance of the stochastic gradient at each iteration and accelerate the rate of convergence. We prove that the proposed algorithm converges linearly in expectation to the solution under a restricted isometry condition. The numerical experiments show that the proposed algorithm has a clearly advantageous balance of efficiency, adaptivity, and accuracy compared with other state-of-the-art greedy algorithms.