  This paper introduces a family of stochastic extragradient-type algorithms
for a class of nonconvex-nonconcave problems characterized by the weak Minty
variational inequality (MVI). Unlike existing results on extragradient methods
in the monotone setting, employing diminishing stepsizes is no longer possible
in the weak MVI setting. This has led to approaches such as increasing batch
sizes per iteration which can however be prohibitively expensive. In contrast,
our proposed methods involves two stepsizes and only requires one additional
oracle evaluation per iteration. We show that it is possible to keep one fixed
stepsize while it is only the second stepsize that is taken to be diminishing,
making it interesting even in the monotone setting. Almost sure convergence is
established and we provide a unified analysis for this family of schemes which
contains a nonlinear generalization of the celebrated primal dual hybrid
gradient algorithm.

Optimization and Control;Machine Learning