  This paper studies decentralized convex-concave minimax optimization problems
of the form $\min_x\max_y f(x,y) \triangleq\frac{1}{m}\sum_{i=1}^m f_i(x,y)$,
where $m$ is the number of agents and each local function can be written as
$f_i(x,y)=\frac{1}{n}\sum_{j=1}^n f_{i,j}(x,y)$. We propose a novel
decentralized optimization algorithm, called multi-consensus stochastic
variance reduced extragradient, which achieves the best known stochastic
first-order oracle (SFO) complexity for this problem. Specifically, each agent
requires $\mathcal O((n+\kappa\sqrt{n})\log(1/\varepsilon))$ SFO calls for
strongly-convex-strongly-concave problem and $\mathcal
O((n+\sqrt{n}L/\varepsilon)\log(1/\varepsilon))$ SFO call for general
convex-concave problem to achieve $\varepsilon$-accurate solution in
expectation, where $\kappa$ is the condition number and $L$ is the smoothness
parameter. The numerical experiments show the proposed method performs better
than baselines.
