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An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization
Lesi Chen, Haishan Ye, Luo Luo
This paper studies the stochastic nonconvex-strongly-concave minimax optimization over a multi-agent network. We propose an efficient algorithm, called Decentralized Recursive gradient descEnt Ascent Method (DREAM), which achieves the best-known theoretical guarantee for finding the ϵ-stationary points. Concretely, it requires 𝒪(min(κ³ϵ⁻³,κ² √(N) ϵ⁻² )) stochastic first-order oracle (SFO) calls and 𝒪̃(κ² ϵ⁻²) communication rounds, where κ is the condition number and N is the total number of individual functions. Our numerical experiments also validate the superiority of DREAM over previous methods.
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