  We consider distributed stochastic variational inequalities (VIs) on
unbounded domains with the problem data that is heterogeneous (non-IID) and
distributed across many devices. We make a very general assumption on the
computational network that, in particular, covers the settings of fully
decentralized calculations with time-varying networks and centralized
topologies commonly used in Federated Learning. Moreover, multiple local
updates on the workers can be made for reducing the communication frequency
between the workers. We extend the stochastic extragradient method to this very
general setting and theoretically analyze its convergence rate in the
strongly-monotone, monotone, and non-monotone (when a Minty solution exists)
settings. The provided rates explicitly exhibit the dependence on network
characteristics (e.g., mixing time), iteration counter, data heterogeneity,
variance, number of devices, and other standard parameters. As a special case,
our method and analysis apply to distributed stochastic saddle-point problems
(SPP), e.g., to the training of Deep Generative Adversarial Networks (GANs) for
which decentralized training has been reported to be extremely challenging. In
experiments for the decentralized training of GANs we demonstrate the
effectiveness of our proposed approach.
