Frank-Wolfe Algorithms for Saddle Point Problems

Gauthier Gidel 1 Tony Jebara 2 Simon Lacoste-Julien 3
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
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.
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Communication dans un congrès
The 20th International Conference on Artificial Intelligence and Statistics, Apr 2017, Fort Lauderdale, Florida, United States. 〈http://www.aistats.org/〉
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https://hal.archives-ouvertes.fr/hal-01403348
Contributeur : Gauthier Gidel <>
Soumis le : vendredi 25 novembre 2016 - 17:46:03
Dernière modification le : jeudi 26 avril 2018 - 10:29:04

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  • HAL Id : hal-01403348, version 1
  • ARXIV : 1610.07797

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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. 〈http://www.aistats.org/〉. 〈hal-01403348〉

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