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Poster
Learning Two-Player Markov Games: Neural Function Approximation and Correlated Equilibrium
Chris Junchi Li · Dongruo Zhou · Quanquan Gu · Michael Jordan
We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is how to do exploration in the high-dimensional function space. We propose a novel online learning algorithm to find a Nash equilibrium by minimizing the duality gap. At the core of our algorithms are upper and lower confidence bounds that are derived based on the principle of optimism in the face of uncertainty. We prove that our algorithm is able to attain an $O(\sqrt{T})$ regret with polynomial computational complexity, under very mild assumptions on the reward function and the underlying dynamic of the Markov Games. We also propose several extensions of our algorithm, including an algorithm with Bernstein-type bonus that can achieve a tighter regret bound, and another algorithm for model misspecification that can be applied to neural network function approximation.
Author Information
Chris Junchi Li (UC Berkeley)
Dongruo Zhou (UCLA)
Quanquan Gu (UCLA)
Michael Jordan (UC Berkeley)
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John Duchi · Michael Jordan · Martin J Wainwright -
2012 Poster: Ancestor Sampling for Particle Gibbs »
Fredrik Lindsten · Michael Jordan · Thomas Schön -
2012 Oral: Privacy Aware Learning »
John Duchi · Michael Jordan · Martin J Wainwright -
2012 Poster: Finite Sample Convergence Rates of Zero-Order Stochastic Optimization Methods »
John Duchi · Michael Jordan · Martin J Wainwright · Andre Wibisono -
2012 Poster: Small-Variance Asymptotics for Exponential Family Dirichlet Process Mixture Models »
Ke Jiang · Brian Kulis · Michael Jordan -
2011 Workshop: Big Learning: Algorithms, Systems, and Tools for Learning at Scale »
Joseph E Gonzalez · Sameer Singh · Graham Taylor · James Bergstra · Alice Zheng · Misha Bilenko · Yucheng Low · Yoshua Bengio · Michael Franklin · Carlos Guestrin · Andrew McCallum · Alexander Smola · Michael Jordan · Sugato Basu -
2011 Poster: Bayesian Bias Mitigation for Crowdsourcing »
Fabian L Wauthier · Michael Jordan -
2011 Poster: Divide-and-Conquer Matrix Factorization »
Lester W Mackey · Ameet S Talwalkar · Michael Jordan -
2010 Oral: Tree-Structured Stick Breaking for Hierarchical Data »
Ryan Adams · Zoubin Ghahramani · Michael Jordan -
2010 Invited Talk: Statistical Inference of Protein Structure and Function »
Michael Jordan -
2010 Poster: Tree-Structured Stick Breaking for Hierarchical Data »
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