Frank-Wolfe Algorithms for Saddle Point Problems

Gauthier Gidel (1) , Tony Jebara (2) , Simon Lacoste-Julien (3)

1 SIERRA - Statistical Machine Learning and Parsimony
2 Columbia University [New York]
3 DIRO - Département d'Informatique et de Recherche Opérationnelle [Montreal]

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.

Mots clés: Structured learning; Games theory; Convex optimization; Saddle Points; Constrained optimization

Domaines: Optimisation et contrôle [math.OC]; Apprentissage [cs.LG]; Machine Learning [stat.ML]

Gauthier Gidel, Tony Jebara, Simon Lacoste-Julien. Frank-Wolfe Algorithms for Saddle Point Problems. The 20th International Conference on Artificial Intelligence and Statistics, Apr 2017, Fort Lauderdale, Florida, United States. ⟨hal-01403348⟩