  We provide a template to derive convergence rates for the following popular
versions of the Frank-Wolfe algorithm on polytopes: vanilla Frank-Wolfe,
Frank-Wolfe with away steps, Frank-Wolfe with blended pairwise steps, and
Frank-Wolfe with in-face directions. Our template shows how the convergence
rates follow from two affine-invariant properties of the problem, namely, error
bound and extended curvature. These properties depend solely on the polytope
and objective function but not on any affine-dependent object like norms. For
each one of the above algorithms, we derive rates of convergence ranging from
sublinear to linear depending on the degree of the error bound.
