Approximate FW Algorithm with a novel DMO method over Graph-structured Support Set

TL;DR

This paper reviews and extends an approximate Frank-Wolfe algorithm for graph-structured convex optimization, introducing a backtracking line-search method that reduces iterations and a new DMO method with limited improvements.

Contribution

The paper presents a novel DMO method (Top-g+ optimal visiting) and an effective backtracking line-search technique for the approximate FW algorithm on GSCO problems.

Findings

Backtracking line-search reduces iteration count.

New DMO method shows limited performance gains.

Original algorithm implementation validated.

Abstract

In this project, we reviewed a paper that deals graph-structured convex optimization (GSCO) problem with the approximate Frank-Wolfe (FW) algorithm. We analyzed and implemented the original algorithm and introduced some extensions based on that. Then we conducted experiments to compare the results and concluded that our backtracking line-search method effectively reduced the number of iterations, while our new DMO method (Top-g+ optimal visiting) did not make satisfying enough improvements.