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

TL;DR

It is concluded that the backtracking line-search method effectively reduced the number of iterations, while the new DMO method (Top-g+ optimal visiting) did not make satisfying enough improvements.

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.

Figures (7)

• Figure 1: An element of a $g$-subgraph model $\mathbb{M}(\mathbb{G}, s=5, g=4)$ defined on a 10-node graph where each colored region is a subgraph.
• Figure 2: Objective function values for the Frank-Wolfe method via DMO, the random projected gradient descent method, and the best-projected gradient descent by comparing all possible cases.
• Figure 3: Convergence plot for the Frank-Wolfe method via DMO, the random projected gradient descent method, and the best-projected gradient descent by comparing all possible cases.
• Figure 4: Objective function values for the Frank-Wolfe methods via DMO, without and with backtracking line-search.
• Figure 5: Convergence plot for the Frank-Wolfe methods via DMO, without and with backtracking line-search.