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We consider a class of non-smooth strongly convex-strongly concave saddlepoint problems in a decentralized setting without a central server. To solve aconsensus formulation of problems in this class, we develop an inexact primaldual hybrid gradient (inexact PDHG) procedure that allows generic gradientcomputation oracles to update the primal and dual variables. We firstinvestigate the performance of inexact PDHG with stochastic variance reductiongradient (SVRG) oracle. Our numerical study uncovers a significant phenomenonof initial conservative progress of iterates of IPDHG with SVRG oracle. Totackle this, we develop a simple and effective switching idea, where ageneralized stochastic gradient (GSG) computation oracle is employed to hastenthe iterates' progress to a saddle point solution during the initial phase ofupdates, followed by a switch to the SVRG oracle at an appropriate juncture.The proposed algorithm is named Decentralized Proximal Switching StochasticGradient method with Compression (C-DPSSG), and is proven to converge to an$\epsilon$-accurate saddle point solution with linear rate. Apart fromdelivering highly accurate solutions, our study reveals that utilizing the bestconvergence phases of GSG and SVRG oracles makes C-DPSSG well suited forobtaining solutions of low/medium accuracy faster, useful for certainapplications. Numerical experiments on two benchmark machine learningapplications show C-DPSSG's competitive performance which validate ourtheoretical findings. The codes used in the experiments can be found\href{https://github.com/chhavisharma123/C-DPSSG-CDC2023}{here}.

Switch and Conquer: Efficient Algorithms By Switching Stochastic Gradient Oracles For Decentralized Saddle Point Problems