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Heavy Ball Momentum for Conditional Gradient
Bingcong Li · Alireza Sadeghi · Georgios Giannakis

Thu Dec 09 08:30 AM -- 10:00 AM (PST) @

Conditional gradient, aka Frank Wolfe (FW) algorithms, have well-documented merits in machine learning and signal processing applications. Unlike projection-based methods, momentum cannot improve the convergence rate of FW, in general. This limitation motivates the present work, which deals with heavy ball momentum, and its impact to FW. Specifically, it is established that heavy ball offers a unifying perspective on the primal-dual (PD) convergence, and enjoys a tighter \textit{per iteration} PD error rate, for multiple choices of step sizes, where PD error can serve as the stopping criterion in practice. In addition, it is asserted that restart, a scheme typically employed jointly with Nesterov's momentum, can further tighten this PD error bound. Numerical results demonstrate the usefulness of heavy ball momentum in FW iterations.

Author Information

Bingcong Li (University of Minnesota, Twin Cities)
Alireza Sadeghi (University of Minnesota, Minneapolis)
Georgios Giannakis (University of Minnesota)

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