  Projection-free conditional gradient (CG) methods are the algorithms of
choice for constrained optimization setups in which projections are often
computationally prohibitive but linear optimization over the constraint set
remains computationally feasible. Unlike in projection-based methods, globally
accelerated convergence rates are in general unattainable for CG. However, a
very recent work on Locally accelerated CG (LaCG) has demonstrated that local
acceleration for CG is possible for many settings of interest. The main
downside of LaCG is that it requires knowledge of the smoothness and strong
convexity parameters of the objective function. We remove this limitation by
introducing a novel, Parameter-Free Locally accelerated CG (PF-LaCG) algorithm,
for which we provide rigorous convergence guarantees. Our theoretical results
are complemented by numerical experiments, which demonstrate local acceleration
and showcase the practical improvements of PF-LaCG over non-accelerated
algorithms, both in terms of iteration count and wall-clock time.
