Title: An Entropic Frank-Wolfe Method

Abstract: The Frank-Wolfe algorithm is an optimisation method for finding the minimum or maximum of a differentiable function on a convex set. It has enjoyed a resurgence in recent years in the machine learning community due to its generic applicability and its ability to provide sparse solutions. Concurrently, the use of entropy as a regulariser for solving constrained linear optimisation has also experienced a resurgence, particularly in the context of computing optimal transport problems and Wasserstein metrics. We propose the insertion of entropy in the linear step of the Frank Wolfe method as a means to obtain approximate solutions at great speed. To demonstrate convergence properties there is an interesting exploration of the dual characterisation of entropy. We demonstrate this lightning-fast method on a handful of optimisation problems.