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Stochastic Gradient Descent-Ascent (SGDA) is one of the most prominentalgorithms for solving min-max optimization and variational inequalitiesproblems (VIP) appearing in various machine learning tasks. The success of themethod led to several advanced extensions of the classical SGDA, includingvariants with arbitrary sampling, variance reduction, coordinate randomization,and distributed variants with compression, which were extensively studied inthe literature, especially during the last few years. In this paper, we proposea unified convergence analysis that covers a large variety of stochasticgradient descent-ascent methods, which so far have required differentintuitions, have different applications and have been developed separately invarious communities. A key to our unified framework is a parametric assumptionon the stochastic estimates. Via our general theoretical framework, we eitherrecover the sharpest known rates for the known special cases or tighten them.Moreover, to illustrate the flexibility of our approach we develop several newvariants of SGDA such as a new variance-reduced method (L-SVRGDA), newdistributed methods with compression (QSGDA, DIANA-SGDA, VR-DIANA-SGDA), and anew method with coordinate randomization (SEGA-SGDA). Although variants of thenew methods are known for solving minimization problems, they were neverconsidered or analyzed for solving min-max problems and VIPs. We alsodemonstrate the most important properties of the new methods through extensivenumerical experiments.

Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods