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Owing to their stability and convergence speed, extragradient methods havebecome a staple for solving large-scale saddle-point problems in machinelearning. The basic premise of these algorithms is the use of an extrapolationstep before performing an update; thanks to this exploration step,extra-gradient methods overcome many of the non-convergence issues that plaguegradient descent/ascent schemes. On the other hand, as we show in this paper,running vanilla extragradient with stochastic gradients may jeopardize itsconvergence, even in simple bilinear models. To overcome this failure, weinvestigate a double stepsize extragradient algorithm where the explorationstep evolves at a more aggressive time-scale compared to the update step. Weshow that this modification allows the method to converge even with stochasticgradients, and we derive sharp convergence rates under an error boundcondition.

Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling