Parameter-free Locally Accelerated Conditional Gradients
This work addresses a key bottleneck for researchers and practitioners in constrained optimization where projections are costly, by making acceleration more accessible without parameter tuning, though it is incremental as it builds on existing locally accelerated CG methods.
The paper tackles the limitation of requiring prior knowledge of smoothness and strong convexity parameters in locally accelerated conditional gradient methods by introducing a parameter-free algorithm, PF-LaCG, which achieves local acceleration and shows practical improvements in iteration count and wall-clock time over non-accelerated methods.
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.