On the Convergence of Stochastic Extragradient for Bilinear Games using Restarted Iteration Averaging
This work addresses convergence issues in stochastic bilinear games for optimization and machine learning applications, representing an incremental improvement over basic SEG methods.
The paper tackles the stochastic bilinear minimax optimization problem by analyzing the same-sample Stochastic ExtraGradient (SEG) method with constant step size, showing that adding iteration averaging enables convergence to the Nash equilibrium, and further improving the rate with scheduled restarting to achieve optimal convergence up to tight constants in interpolation settings.
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. In sharp contrasts with the basic SEG method whose last iterate only contracts to a fixed neighborhood of the Nash equilibrium, SEG augmented with iteration averaging provably converges to the Nash equilibrium under the same standard settings, and such a rate is further improved by incorporating a scheduled restarting procedure. In the interpolation setting where noise vanishes at the Nash equilibrium, 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.