Frank-Wolfe Algorithms for Saddle Point Problems
Abstract
We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solver over polytopes, thereby partially answering a 30 year-old conjecture. We also survey other convergence results and highlight gaps in the theoretical underpinnings of FW-style algorithms. Motivating applications without known efficient alternatives are explored through structured prediction with combinatorial penalties as well as games over matching polytopes involving an exponential number of constraints.
Cite
@article{arxiv.1610.07797,
title = {Frank-Wolfe Algorithms for Saddle Point Problems},
author = {Gauthier Gidel and Tony Jebara and Simon Lacoste-Julien},
journal= {arXiv preprint arXiv:1610.07797},
year = {2017}
}
Comments
Appears in: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS 2017). 39 pages