  Large scale convex-concave minimax problems arise in numerous applications,
including game theory, robust training, and training of generative adversarial
networks. Despite their wide applicability, solving such problems efficiently
and effectively is challenging in the presence of large amounts of data using
existing stochastic minimax methods. We study a class of stochastic minimax
methods and develop a communication-efficient distributed stochastic
extragradient algorithm, LocalAdaSEG, with an adaptive learning rate suitable
for solving convex-concave minimax problems in the Parameter-Server model.
LocalAdaSEG has three main features: (i) a periodic communication strategy that
reduces the communication cost between workers and the server; (ii) an adaptive
learning rate that is computed locally and allows for tuning-free
implementation; and (iii) theoretically, a nearly linear speed-up with respect
to the dominant variance term, arising from the estimation of the stochastic
gradient, is proven in both the smooth and nonsmooth convex-concave settings.
LocalAdaSEG is used to solve a stochastic bilinear game, and train a generative
adversarial network. We compare LocalAdaSEG against several existing optimizers
for minimax problems and demonstrate its efficacy through several experiments
in both homogeneous and heterogeneous settings.
