Parameter-free Locally Accelerated Conditional Gradients

Understand

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.