Decentralized Stochastic Variance Reduced Extragradient Method

• URL: http://arxiv.org/abs/2202.00509v1
• Date: Tue, 1 Feb 2022 16:06:20 GMT
• Title: Decentralized Stochastic Variance Reduced Extragradient Method
• Authors: Luo Luo, Haishan Ye
• Abstract summary: This paper studies decentralized convex-concave minimax optimization problems of the form $min_xmax_y fx,y triqfrac1msumi=1m f_i triqfrac1msumi=1m f_i triqfrac1msumi=1m f_i triqfrac1msumi=1m f_i triqfrac1msum
• Score: 25.21457349137344
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper studies decentralized convex-concave minimax optimization problems of the form $\min_x\max_y f(x,y) \triangleq\frac{1}{m}\sum_{i=1}^m f_i(x,y)$, where $m$ is the number of agents and each local function can be written as $f_i(x,y)=\frac{1}{n}\sum_{j=1}^n f_{i,j}(x,y)$. We propose a novel decentralized optimization algorithm, called multi-consensus stochastic variance reduced extragradient, which achieves the best known stochastic first-order oracle (SFO) complexity for this problem. Specifically, each agent requires $\mathcal O((n+\kappa\sqrt{n})\log(1/\varepsilon))$ SFO calls for strongly-convex-strongly-concave problem and $\mathcal O((n+\sqrt{n}L/\varepsilon)\log(1/\varepsilon))$ SFO call for general convex-concave problem to achieve $\varepsilon$-accurate solution in expectation, where $\kappa$ is the condition number and $L$ is the smoothness parameter. The numerical experiments show the proposed method performs better than baselines.

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