A decentralized algorithm for large scale min-max problems

We consider a distributed saddle point problem, in which a collection of nodes collaboratively optimize a sum of local component functions through local computations and information exchange with neighbouring nodes. To solve this problem, we propose a decentralized algorithm based on the Extragradient method, whose centralized implementation has been shown to achieve good performance on a wide range of min-max problems. We show that our proposed method achieves linear convergence under suitable assumptions and explicitly characterize how the convergence rate depends on the condition number and the spectral gap of the communication graph. We also present numerical simulations that corroborate our theoretical results.