  The Frank Wolfe algorithm (FW) is a popular projection-free alternative for
solving large-scale constrained optimization problems. However, the FW
algorithm suffers from a sublinear convergence rate when minimizing a smooth
convex function over a compact convex set. Thus, exploring techniques that
yield a faster convergence rate becomes crucial. A classic approach to obtain
faster rates is to combine previous iterates to obtain the next iterate. In
this work, we extend this approach to the FW setting and show that the optimal
way to combine the past iterates is using a set of orthogonal Jacobi
polynomials. We also a polynomial-based acceleration technique, referred to as
Jacobi polynomial accelerated FW, which combines the current iterate with the
past iterate using combing weights related to the Jacobi recursion. By
carefully choosing parameters of the Jacobi polynomials, we obtain a faster
sublinear convergence rate. We provide numerical experiments on real datasets
to demonstrate the efficacy of the proposed algorithm.
