Randomization and sparsity in huge-scale optimization on the Mirror Descent example

TL;DR

This paper explores various randomization techniques in mirror descent to maximize the use of sparsity in large-scale convex optimization problems, including a generalization for problems with functional constraints.

Contribution

It introduces a novel randomization approach in mirror descent that leverages problem sparsity and extends to convex problems with functional restrictions.

Findings

Enhanced efficiency in large-scale sparse optimization

Generalized randomization method for constrained convex problems

Potential for improved convergence rates

Abstract

We investigate different randomizations for mirror descent method. We try to propose such a randomization that allows us to use sparsity of the problem as much as it possible. In the paper one can also find a generalization of randomizaed mirror descent for the convex optimization problems with functional restrictions.