Unifying mirror descent and dual averaging

TL;DR

This paper introduces a new family of first-order optimization algorithms that unify mirror descent and dual averaging, offering improved methods for constrained optimization with promising preliminary results.

Contribution

It proposes a novel unified framework that combines mirror descent and dual averaging, leading to new algorithms for constrained optimization.

Findings

Preliminary simulations show significant performance improvements.

The new algorithms outperform existing methods in certain scenarios.

The framework provides a theoretical basis for future algorithm development.

Abstract

We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization that combines the advantages of mirror descent and dual averaging. Our preliminary simulation study shows that these new algorithms significantly outperform available methods in some situations.