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We study the stochastic bilinear minimax optimization problem, presenting an analysis of the same-sample Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the method that yield favorable convergence. We first note that the last iterate of the basic SEG method only contracts to a fixed neighborhood of the Nash equilibrium, independent of the step size. This contrasts sharply with the standard setting of minimization where standard stochastic algorithms converge to a neighborhood that vanishes in proportion to the square-root (constant) step size. Under the same setting, however, we prove that when augmented with iteration averaging, SEG provably converges to the Nash equilibrium, and such a rate is provably accelerated by incorporating a scheduled restarting procedure. In the interpolation setting, we achieve an optimal convergence rate up to tight constants. We present numerical experiments that validate our theoretical findings and demonstrate the effectiveness of the SEG method when equipped with iteration averaging and restarting.
Author Information
Chris Junchi Li (University of California, Berkeley)
Yaodong Yu (UC Berkeley)
Nicolas Loizou (Mila, Université de Montréal)
Gauthier Gidel (Mila)
I am a Ph.D student supervised by Simon Lacoste-Julien, I graduated from ENS Ulm and Université Paris-Saclay. I was a visiting PhD student at Sierra. I also worked for 6 months as a freelance Data Scientist for Monsieur Drive (Acquired by Criteo) and I recently co-founded a startup called Krypto. I'm currently pursuing my PhD at Mila. My work focuses on optimization applied to machine learning. More details can be found in my resume. My research is to develop new optimization algorithms and understand the role of optimization in the learning procedure, in short, learn faster and better. I identify to the field of machine learning (NIPS, ICML, AISTATS and ICLR) and optimization (SIAM OP)
Yi Ma (UC Berkeley)
Nicolas Le Roux perso (Very poor)
Michael Jordan (UC Berkeley)
Related Events (a corresponding poster, oral, or spotlight)
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2021 : On the convergence of stochastic extragradient for bilinear games using restarted iteration averaging »
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Ryan Adams · Zoubin Ghahramani · Michael Jordan -
2010 Spotlight: Variational Inference over Combinatorial Spaces »
Alexandre Bouchard-Côté · Michael Jordan -
2010 Poster: Variational Inference over Combinatorial Spaces »
Alexandre Bouchard-Côté · Michael Jordan -
2010 Poster: Unsupervised Kernel Dimension Reduction »
Meihong Wang · Fei Sha · Michael Jordan -
2010 Poster: Heavy-Tailed Process Priors for Selective Shrinkage »
Fabian L Wauthier · Michael Jordan -
2010 Poster: Random Conic Pursuit for Semidefinite Programming »
Ariel Kleiner · ali rahimi · Michael Jordan -
2009 Workshop: Nonparametric Bayes »
Dilan Gorur · Francois Caron · Yee Whye Teh · David B Dunson · Zoubin Ghahramani · Michael Jordan -
2009 Poster: Sharing Features among Dynamical Systems with Beta Processes »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2009 Oral: Sharing Features among Dynamical Systems with Beta Processes »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2009 Poster: Asymptotically Optimal Regularization in Smooth Parametric Models »
Percy Liang · Francis Bach · Guillaume Bouchard · Michael Jordan -
2009 Poster: Nonparametric Latent Feature Models for Link Prediction »
Kurt T Miller · Tom Griffiths · Michael Jordan -
2009 Spotlight: Nonparametric Latent Feature Models for Link Prediction »
Kurt T Miller · Tom Griffiths · Michael Jordan -
2008 Oral: Shared Segmentation of Natural Scenes Using Dependent Pitman-Yor Processes »
Erik Sudderth · Michael Jordan -
2008 Poster: Nonparametric Bayesian Learning of Switching Linear Dynamical Systems »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2008 Poster: High-dimensional union support recovery in multivariate regression »
Guillaume R Obozinski · Martin J Wainwright · Michael Jordan -
2008 Poster: Shared Segmentation of Natural Scenes Using Dependent Pitman-Yor Processes »
Erik Sudderth · Michael Jordan -
2008 Spotlight: High-dimensional union support recovery in multivariate regression »
Guillaume R Obozinski · Martin J Wainwright · Michael Jordan -
2008 Spotlight: Nonparametric Bayesian Learning of Switching Linear Dynamical Systems »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2008 Poster: Posterior Consistency of the Silverman g-prior in Bayesian Model Choice »
Zhihua Zhang · Michael Jordan · Dit-Yan Yeung -
2008 Poster: DiscLDA: Discriminative Learning for Dimensionality Reduction and Classification »
Simon Lacoste-Julien · Fei Sha · Michael Jordan -
2008 Spotlight: Posterior Consistency of the Silverman g-prior in Bayesian Model Choice »
Zhihua Zhang · Michael Jordan · Dit-Yan Yeung -
2008 Poster: Efficient Inference in Phylogenetic InDel Trees »
Alexandre Bouchard-Côté · Michael Jordan · Dan Klein -
2008 Poster: Spectral Clustering with Perturbed Data »
Ling Huang · Donghui Yan · Michael Jordan · Nina Taft -
2008 Spotlight: Efficient Inference in Phylogenetic InDel Trees »
Alexandre Bouchard-Côté · Michael Jordan · Dan Klein -
2008 Spotlight: Spectral Clustering with Perturbed Data »
Ling Huang · Donghui Yan · Michael Jordan · Nina Taft -
2007 Poster: Agreement-Based Learning »
Percy Liang · Dan Klein · Michael Jordan -
2007 Spotlight: Agreement-Based Learning »
Percy Liang · Dan Klein · Michael Jordan -
2007 Spotlight: Resampling Methods for Protein Structure Prediction with Rosetta »
Ben Blum · David Baker · Michael Jordan · Philip Bradley · Rhiju Das · David Kim -
2007 Spotlight: Estimating divergence functionals and the likelihood ratio by penalized convex risk minimization »
XuanLong Nguyen · Martin J Wainwright · Michael Jordan -
2007 Poster: Resampling Methods for Protein Structure Prediction with Rosetta »
Ben Blum · David Baker · Michael Jordan · Philip Bradley · Rhiju Das · David Kim -
2007 Poster: Estimating divergence functionals and the likelihood ratio by penalized convex risk minimization »
XuanLong Nguyen · Martin J Wainwright · Michael Jordan -
2006 Poster: Distributed PCA and Network Anomaly Detection »
Ling Huang · XuanLong Nguyen · Minos Garofalakis · Michael Jordan · Anthony D Joseph · Nina Taft