  The Stochastic Extragradient (SEG) method is one of the most popular
algorithms for solving min-max optimization and variational inequalities
problems (VIP) appearing in various machine learning tasks. However, several
important questions regarding the convergence properties of SEG are still open,
including the sampling of stochastic gradients, mini-batching, convergence
guarantees for the monotone finite-sum variational inequalities with possibly
non-monotone terms, and others. To address these questions, in this paper, we
develop a novel theoretical framework that allows us to analyze several
variants of SEG in a unified manner. Besides standard setups, like Same-Sample
SEG under Lipschitzness and monotonicity or Independent-Samples SEG under
uniformly bounded variance, our approach allows us to analyze variants of SEG
that were never explicitly considered in the literature before. Notably, we
analyze SEG with arbitrary sampling which includes importance sampling and
various mini-batching strategies as special cases. Our rates for the new
variants of SEG outperform the current state-of-the-art convergence guarantees
and rely on less restrictive assumptions.
