Convergence Behaviour of Some Gradient-Based Methods on Bilinear Zero-Sum Games

08/15/2019 ∙ by Guojun Zhang, et al. ∙ 0 ∙ share

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, and understanding the dynamics of (stochastic) gradient algorithms for solving such formulations has been a grand challenge. As a first step, we restrict ourselves to bilinear zero-sum games and give a systematic analysis of popular gradient updates, for both simultaneous and alternating versions. We provide exact conditions for their convergence and find the optimal parameter setup and convergence rates. In particular, our results offer formal evidence that alternating updates converge "better" than simultaneous ones.

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Convergence Behaviour of Some Gradient-Based Methods on Bilinear Games

Min-max optimization has attracted much attention in the machine learnin...
08/15/2019 ∙ by Guojun Zhang, et al. ∙ 0 ∙ share

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Convergence Behaviour of Some Gradient-Based Methods on Bilinear Zero-Sum Games

Authors

Convergence Behaviour of Some Gradient-Based Methods on Bilinear Games

Complex Momentum for Learning in Games

Stochastic Hamiltonian Gradient Methods for Smooth Games

Stochastic Primal-Dual Algorithms with Faster Convergence than O(1/√(T)) for Problems without Bilinear Structure

LEAD: Least-Action Dynamics for Min-Max Optimization

Average-case Acceleration for Bilinear Games and Normal Matrices

Adaptive extra-gradient methods for min-max optimization and games

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