Stability and Generalization of the Decentralized Stochastic Gradient Descent Ascent Algorithm

• URL: http://arxiv.org/abs/2310.20369v1
• Date: Tue, 31 Oct 2023 11:27:01 GMT
• Title: Stability and Generalization of the Decentralized Stochastic Gradient Descent Ascent Algorithm
• Authors: Miaoxi Zhu, Li Shen, Bo Du, Dacheng Tao
• Abstract summary: We investigate the complexity of the generalization bound of the decentralized gradient descent (D-SGDA) algorithm. Our results analyze the impact of different top factors on the generalization of D-SGDA. We also balance it with the generalization to obtain the optimal convex-concave setting.
• Score: 80.94861441583275
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The growing size of available data has attracted increasing interest in solving minimax problems in a decentralized manner for various machine learning tasks. Previous theoretical research has primarily focused on the convergence rate and communication complexity of decentralized minimax algorithms, with little attention given to their generalization. In this paper, we investigate the primal-dual generalization bound of the decentralized stochastic gradient descent ascent (D-SGDA) algorithm using the approach of algorithmic stability under both convex-concave and nonconvex-nonconcave settings. Our theory refines the algorithmic stability in a decentralized manner and demonstrates that the decentralized structure does not destroy the stability and generalization of D-SGDA, implying that it can generalize as well as the vanilla SGDA in certain situations. Our results analyze the impact of different topologies on the generalization bound of the D-SGDA algorithm beyond trivial factors such as sample sizes, learning rates, and iterations. We also evaluate the optimization error and balance it with the generalization gap to obtain the optimal population risk of D-SGDA in the convex-concave setting. Additionally, we perform several numerical experiments which validate our theoretical findings.

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