Adaptive Variant of Frank-Wolfe Method for Relative Smooth Convex Optimization Problems

TL;DR

This paper presents an adaptive Frank-Wolfe algorithm variant that employs Bregman divergence for step-size calculation, demonstrating improved convergence and performance over traditional methods in relatively smooth convex optimization.

Contribution

The paper introduces a novel adaptive Frank-Wolfe method using Bregman divergence, with proven convergence and superior performance in certain convex optimization problems.

Findings

Algorithm converges under triangle scaling property.

Outperforms Euclidean-based Frank-Wolfe in experiments.

Better than accelerated gradient methods in specific cases.

Abstract

The paper introduces a new adaptive version of the Frank-Wolfe algorithm for relatively smooth convex functions. It is proposed to use the Bregman divergence other than half the square of the Euclidean norm in the formula for step-size. Algorithm convergence estimates for minimization problems of relatively smooth convex functions with the triangle scaling property are proved. Computational experiments are performed, and conditions are shown in which the obvious advantage of the proposed algorithm over its Euclidean norm analogue is shown. We also found examples of problems for which the proposed variation of the Frank-Wolfe method works better than known accelerated gradient-type methods for relatively smooth convex functions with the triangle scaling property.