Simple steps are all you need: FrankWolfe and generalized selfconcordant functions
Abstract
Generalized selfconcordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple FrankWolfe variant that uses the openloop step size strategy $\gamma_t = 2/(t+2)$, obtaining a $\mathcal{O}(1/t)$ convergence rate for this class of functions in terms of primal gap and FrankWolfe gap, where $t$ is the iteration count. This avoids the use of secondorder information or the need to estimate local smoothness parameters of previous work. We also show improved convergence rates for various common cases, e.g., when the feasible region under consideration is uniformly convex or polyhedral.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.13913
 Bibcode:
 2021arXiv210513913C
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Machine Learning;
 Statistics  Machine Learning