  In this paper, we study active set identification results for the away-step
Frank-Wolfe algorithm in different settings. We first prove a local
identification property that we apply, in combination with a convergence
hypothesis, to get an active set identification result. We then prove, in the
nonconvex case, a novel $O(1/\sqrt{k})$ convergence rate result and active set
identification for different stepsizes (under suitable assumptions on the set
of stationary points). By exploiting those results, we also give explicit
active set complexity bounds for both strongly convex and nonconvex objectives.
While we initially consider the probability simplex as feasible set, in the
appendix we show how to adapt some of our results to generic polytopes.
