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arXiv · 2212.02387

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

Lesi Chen·Haishan Ye·Luo Luo
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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 $ε$-stationary points. Concretely, it requires $\mathcal{O}(\min (κ^3ε^{-3},κ^2 \sqrt{N} ε^{-2} ))$ stochastic first-order oracle (SFO) calls and $\tilde{\mathcal{O}}(κ^2 ε^{-2})$ 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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Lesi Chen, Haishan Ye, Luo Luo. 2024-05-14. An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization. https://arxiv.org/abs/2212.02387

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