May 15, 2024, 4:43 a.m. | Lesi Chen, Haishan Ye, Luo Luo

cs.LG updates on arXiv.org arxiv.org

arXiv:2212.02387v4 Announce Type: replace
Abstract: 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 $\epsilon$-stationary points. Concretely, it requires $\mathcal{O}(\min (\kappa^3\epsilon^{-3},\kappa^2 \sqrt{N} \epsilon^{-2} ))$ stochastic first-order oracle (SFO) calls and $\tilde{\mathcal{O}}(\kappa^2 \epsilon^{-2})$ communication rounds, where $\kappa$ is the condition number and $N$ is the total number of individual functions. Our numerical experiments also validate the …

abstract agent algorithm arxiv cs.lg decentralized epsilon gradient math.oc min minimax multi-agent network optimization paper recursive replace stochastic studies type

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