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Parameter-free Locally Accelerated Conditional Gradients
Alejandro Carderera · Jelena Diakonikolas · Cheuk Yin Lin · Sebastian Pokutta

Tue Jul 20 06:30 AM -- 06:35 AM (PDT) @ None

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.

Author Information

Alejandro Carderera (Georgia Institute of Technology)

I am a third year Ph.D. student in Machine Learning at the Georgia Institute of Technology, working with Prof. Sebastian Pokutta. My work is currently aimed at designing novel convex optimization algorithms with solid theoretical convergence guarantees and good numerical performance. Prior to joining the Ph.D. program I worked at HP as an R&D Systems Engineer for two years. I obtained a bachelor of science in Industrial Engineering from the Universidad Politécnica de Madrid and a Master of Science in Applied Physics from Cornell University.

Jelena Diakonikolas (University of Wisconsin-Madison)
Cheuk Yin Lin (University of Wisconsin–Madison)
Sebastian Pokutta (ZIB/TUB)

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