An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization

arXiv2212.02387MaRDI QIDQ6419592

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Publication date: 5 December 2022

Abstract: This paper studies the stochastic optimization for decentralized nonconvex-strongly-concave minimax problem. We propose a simple and efficient algorithm, called Decentralized Recursive-gradient descEnt Ascent Method ( exttt{DREAM}), which achieves the best-known theoretical guarantee for finding the $epsilon$-stationary point of the primal function. For the online setting, the proposed method requires $mathcalO(kapp{a}^{3}epsilo{n}^{-3})$ stochastic first-order oracle (SFO) calls and $$ communication rounds to find an $epsilon$-stationary point, where $kappa$ is the condition number and $lambd{a}_2(W)$ is the second-largest eigenvalue of the gossip matrix~$W$. For the offline setting with totally $N$ component functions, the proposed method requires $$ SFO calls and the same communication complexity as the online setting.

Has companion code repository: https://github.com/TrueNobility303/DREAM

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